diff --git a/src/opt/mpi/include/rrange.cc.h b/src/opt/mpi/include/rrange.cc.h
index d3152fa..e2663d4 100644
--- a/src/opt/mpi/include/rrange.cc.h
+++ b/src/opt/mpi/include/rrange.cc.h
@@ -19,6 +19,10 @@ namespace CNORXZ
     namespace mpi
     {
 
+	/*==============+
+	 |    RIndex    |
+	 +==============*/
+
 	template <class IndexI, class IndexK>
 	RIndex<IndexI,IndexK>::RIndex(const RIndex& in) :
 	    mRange(in.mRange),
@@ -50,193 +54,274 @@ namespace CNORXZ
 	template <class IndexI, class IndexK>
 	RIndex<IndexI,IndexK>::RIndex(const Sptr<Index>& local) :
 	{
+	    CXZ_ERROR("not implemented");
 	    //!!!
 	}
 	    
 	template <class IndexI, class IndexK>
 	RIndex<IndexI,IndexK>& RIndex<IndexI,IndexK>::operator=(SizeT pos)
 	{
+	    IB::mPos = pos; // = lex
+	    if(lexpos >= lmax().val()){
+		IB::mPos = pmax().val();
+		return *this;
+	    }
 	    // pos is the lexicographic position of the global range.
 	    // Hence, have to consider the rank geometry.
-	    if constexpr(has_static_sub<IndexI>::value or has_static_sub<IndexK>::value){
-		
+	    const auto& i = mI->pack();
+	    const auto& k = mK->pack();
+	    const auto& ilf = mI->lexFormat();
+	    const auto& klf = mK->lexFormat();
+	    SizeT r = 0;
+	    SizeT l = 0;
+	    if constexpr(has_static_sub<IndexI>::value){
+		constexpr SizeT NI = index_dim<IndexI>::value;
+		iter<0,NI>( [&](auto mu) {
+		    const SizeT jmu = (IB::mPos / ilf[mu].val()*klf[mu].val()) %
+			i[mu]->lmax().val()*k[mu]->lmax().val();
+		    r += ( jmu / i[mu]->lmax().val() ) * klf[mu].val();
+		    l += ( jmu % i[mu]->lmax().val() ) * ilf[mu].val();
+		}, NoF{} );
+	    }
+	    else if constexpr( has_static_sub<IndexK>::value){
+		constexpr SizeT NI = index_dim<IndexK>::value;
+		iter<0,NI>( [&](auto mu) {
+		    const SizeT jmu = (IB::mPos / ilf[mu].val()*klf[mu].val()) %
+			i[mu]->lmax().val()*k[mu]->lmax().val();
+		    r += ( jmu / i[mu]->lmax().val() ) * klf[mu].val();
+		    l += ( jmu % i[mu]->lmax().val() ) * ilf[mu].val();
+		}, NoF{} );
 	    }
 	    else {
-
+		const SizeT NI = mI->dim();
+		for(SizeT mu = 0; mu != NI; ++mu){
+		    const SizeT jmu = (IB::mPos / ilf[mu].val()*klf[mu].val()) %
+			i[mu]->lmax().val()*k[mu]->lmax().val();
+		    r += ( jmu / i[mu]->lmax().val() ) * klf[mu].val();
+		    l += ( jmu % i[mu]->lmax().val() ) * ilf[mu].val();
+		}
 	    }
+	    *mI = l;
+	    *mK = r;
 	    return *this;
 	}
 
 	template <class IndexI, class IndexK>
 	RIndex<IndexI,IndexK>& RIndex<IndexI,IndexK>::operator++()
 	{
-	    
+	    *this = lex() + 1; // room for optimization
 	    return *this;
 	}
 
 	template <class IndexI, class IndexK>
 	RIndex<IndexI,IndexK>& RIndex<IndexI,IndexK>::operator--()
 	{
-
+	    *this = lex() - 1; // room for optimization
 	    return *this;
 	}
 
 	template <class IndexI, class IndexK>
 	RIndex<IndexI,IndexK> RIndex<IndexI,IndexK>::operator+(Int n) const
 	{
-
+	    RIndex<IndexI,IndexK> o(*this);
+	    return o += n;
 	}
 
 	template <class IndexI, class IndexK>
 	RIndex<IndexI,IndexK> RIndex<IndexI,IndexK>::operator-(Int n) const
 	{
-
+	    RIndex<IndexI,IndexK> o(*this);
+	    return o -= n;
 	}
 
 	template <class IndexI, class IndexK>
 	SizeT RIndex<IndexI,IndexK>::operator-(const RIndex& i) const
 	{
-
+	    return lex() - i.lex();
 	}
 
 	template <class IndexI, class IndexK>
 	RIndex<IndexI,IndexK>& RIndex<IndexI,IndexK>::operator+=(Int n)
 	{
-
+	    *this = lex() + n;
 	    return *this;
 	}
 
 	template <class IndexI, class IndexK>
 	RIndex<IndexI,IndexK>& RIndex<IndexI,IndexK>::operator-=(Int n)
 	{
-
+	    *this = lex() - n;
 	    return *this;
 	}
 
 	template <class IndexI, class IndexK>
 	SizeT RIndex<IndexI,IndexK>::lex() const
 	{
-
+	    return IB::mPos;
 	}
 
 	template <class IndexI, class IndexK>
 	constexpr RIndex<IndexI,IndexK>::decltype(auto) pmax() const
 	{
-
+	    return mK->lmax().val() * mI->lmax().val();
 	}
-	    
 
 	template <class IndexI, class IndexK>
 	constexpr RIndex<IndexI,IndexK>::decltype(auto) lmax() const
 	{
-
+	    return mK->lmax().val() * mI->lmax().val();
 	}
 
 	template <class IndexI, class IndexK>
 	IndexId<0> RIndex<IndexI,IndexK>::id() const
 	{
-
+	    return IndexId<0>(this->ptrId());
 	}
 
 	template <class IndexI, class IndexK>
 	MetaType RIndex<IndexI,IndexK>::operator*() const
 	{
-
+	    return meta();
 	}
 	
 	template <class IndexI, class IndexK>
 	constexpr SizeT RIndex<IndexI,IndexK>::dim() const
 	{
-
+	    return mI->dim();
 	}
 
 	template <class IndexI, class IndexK>
 	Sptr<RangeType> RIndex<IndexI,IndexK>::range() const
 	{
-
+	    return mRange;
 	}
 
 	template <class IndexI, class IndexK>
 	template <SizeT I>
 	decltype(auto) RIndex<IndexI,IndexK>::stepSize(const IndexId<I>& id) const
 	{
-
+	    return mK->stepSize(id) * mI->lmax().val() + mI->stepSize(id);
 	}
 
 	template <class IndexI, class IndexK>
 	String RIndex<IndexI,IndexK>::stringMeta() const
 	{
-
+	    const SizeT r = mK->lex();
+	    String o;
+	    broadcast(r, mI->stringMeta(), &o);
+	    return o;
 	}
 
 	template <class IndexI, class IndexK>
 	MetaType RIndex<IndexI,IndexK>::meta() const
 	{
-
+	    const SizeT r = mK->lex();
+	    MetaType o;
+	    broadcast(r, mI->meta(), &o);
+	    return o;
 	}
 
 	template <class IndexI, class IndexK>
 	RIndex<IndexI,IndexK>& RIndex<IndexI,IndexK>::at(const MetaType& metaPos)
 	{
-
+	    CXZ_ERROR("not implemented");
+	    return *this;
 	}
 
 	template <class IndexI, class IndexK>
 	RangePtr RIndex<IndexI,IndexK>::prange(const RIndex<IndexI,IndexK>& last) const
 	{
-
+	    CXZ_ERROR("not implemented");
+	    return nullptr;
 	}
 
 	template <class IndexI, class IndexK>
 	auto RIndex<IndexI,IndexK>::deepFormat() const
 	{
-
+	    return concat( mul(mK->deepFormat(), mI->lmax().val() ), mI->deepFormat() );
 	}
 
 	template <class IndexI, class IndexK>
 	auto RIndex<IndexI,IndexK>::deepMax() const
 	{
-
+	    return concat( mK->deepMax(), mI->deepMax() );
 	}
 
 	template <class IndexI, class IndexK>
 	RIndex<IndexI,IndexK>& RIndex<IndexI,IndexK>::reformat(const Vector<SizeT>& f, const Vector<SizeT>& s)
 	{
-
+	    CXZ_ERROR("not implemented");
+	    return *this;
 	}
 
 	template <class IndexI, class IndexK>
 	template <class Xpr, class F>
 	constexpr decltype(auto) RIndex<IndexI,IndexK>::ifor(const Xpr& xpr, F&& f) const
 	{
-
+	    CXZ_ERROR("not implemented");
+	    return 0;
 	}
 
 	template <class IndexI, class IndexK>
 	bool RIndex<IndexI,IndexK>::formatIsTrivial() const
 	{
-
+	    return mI->formatIsTrivial();
 	}
 
 	template <class IndexI, class IndexK>
 	decltype(auto) RIndex<IndexI,IndexK>::xpr(const Sptr<RIndex<IndexI,IndexK>>& _this) const
 	{
-
+	    CXZ_ERROR("not implemented");
+	    return 0;
 	}
 
 	template <class IndexI, class IndexK>
-	int RIndex<IndexI,IndexK>::rank() const
+	SizeT RIndex<IndexI,IndexK>::rank() const
 	{
-
+	    return mK->lex();
 	}
 
 	template <class IndexI, class IndexK>
 	Sptr<Index> RIndex<IndexI,IndexK>::local() const
 	{
-
+	    return mI;
 	}
 	
 	
+	/*=====================+
+	 |    RRangeFactory    |
+	 +=====================*/
+
+	template <class RangeI, class RangeK>
+	RRangeFactory<RangeI,RangeK>::RRangeFactory(const Sptr<RangeI>& ri,
+						    const Sptr<RangeK>& rk):
+	    mRI(ri),
+	    mRK(rk)
+	{
+	    if constexpr(has_static_sub<typename RangeI::IndexType>::value and
+			 has_static_sub<typename RangeK::IndexType>::value) {
+		static_assert(typename RangeI::NR == typename RangeK::NR,
+			      "ranges have to be of same dimension");
+	    }
+	    else {
+		CXZ_ASSERT(ri->dim() == rk->dim(), "ranges have to be of same dimension, got "
+			   << ri->dim() << " and " << rk->dim());
+	    }
+	}
+
+	template <class RangeI, class RangeK>
+	void RRangeFactory<RangeI,RangeK>::make()
+	{
+	    Vector<Uuid> key = { mRI->key(), mRK->key() };
+	    const auto& info = typeid(RRange<RangeI,RangeK>);
+	    mProd = this->fromCreated(info, key);
+	    if(mProd == nullptr) {
+		mProd = std::shared_ptr<RRange<RangeI,RangeK>>
+		    ( new RRange<RangeI,RangeK>(mRI, mRK) );
+		this->addToCreated(info, key, mProd);
+	    }
+	}
+
     } // namespace mpi
 } // namespace CNORXZ
 
diff --git a/src/opt/mpi/include/rrange.h b/src/opt/mpi/include/rrange.h
index 7b0caf0..8503ccf 100644
--- a/src/opt/mpi/include/rrange.h
+++ b/src/opt/mpi/include/rrange.h
@@ -26,12 +26,12 @@ namespace CNORXZ
 	    @tparam IndexK Index type used to indicate the rank.
 	*/
 	template <class IndexI, class IndexK>
-	class RIndex : public IndexInterface<RIndex<IndexI,IndexK>,typename Index::MetaType>
+	class RIndex : public IndexInterface<RIndex<IndexI,IndexK>,typename IndexI::MetaType>
 	{
 	public:
-	    typedef IndexInterface<RIndex<IndexI,IndexK>,typename Index::MetaType> IB;
-	    typedef typename Index::MetaType MetaType;
-	    typedef RRange<typename Index::RangeType> RangeType;
+	    typedef IndexInterface<RIndex<IndexI,IndexK>,typename IndexI::MetaType> IB;
+	    typedef typename IndexI::MetaType MetaType;
+	    typedef RRange<typename IndexI::RangeType,typename IndexK::RangeType> RangeType;
 
 	    INDEX_RANDOM_ACCESS_ITERATOR_DEFS(MetaType);
 
@@ -141,7 +141,7 @@ namespace CNORXZ
 	    decltype(auto) xpr(const Sptr<RIndex<IndexI,IndexK>>& _this) const;
 
 	    /** Get the current rank. */
-	    int rank() const;
+	    SizeT rank() const;
 
 	    /** Get the local index on THIS rank. */
 	    Sptr<IndexI,IndexK> local() const;
@@ -149,24 +149,48 @@ namespace CNORXZ
 	
 	private:
 	    Sptr<RangeType> mRange; /**< RRange. */
-	    Sptr<IndexI> mJ; /**< Index on the local range of the THIS rank. */
+	    Sptr<IndexI> mI; /**< Index on the local range of the THIS rank. */
 	    Sptr<IndexK> mK; /**< Multi-index indicating the current rank. */
 	    //!!!
 	};
 
-	// Factory!!!
+	// Traits!!!
+	
+	/** ****
+	    Specific factory for RRange.
+	    @tparam RangeI Local range type.
+	    @tparam RangeK Geometry range type.
+	 */
+	template <class RangeI, class RangeK>
+	class RRangeFactory : public RangeFactoryBase
+	{
+	public:
+	    /** Construct and setup factory.
+		@param ri Local range.
+		@param rk Geometry range.
+	     */
+	    RRangeFactory(const Sptr<RangeI>& ri, const Sptr<RangeK>& rk);
+	    
+	private:
+	    RRangeFactory() = default;
+	    virtual void make() override final;
+
+	    Sptr<RangeI> mRI;
+	    Sptr<RangeK> mRK;
+	};	
 
 	/** ****
 	    Range-Wrapper for ranges that are distributed on MPI ranks.
-	    @tparam Range Local range type.
+	    @tparam RangeI Local range type.
+	    @tparam RangeK Geometry range type.
 	*/
-	template <class Range>
-	class RRange : public RangeInterface<RRange<Range>>
+	template <class RangeI, class RangeK>
+	class RRange : public RangeInterface<RRange<RangeI,RangeK>>
 	{
 	public:
 	    typedef RangeBase RB;
-	    typedef RIndex<typename Range::IndexType> IndexType;
-	    typedef typename Range::MetaType MetaType;
+	    typedef RIndex<typename RangeI::IndexType,typename RangeK::IndexType> IndexType;
+	    typedef typename RangeI::MetaType MetaType;
 
 	    friend RRangeFactory<Range>;
 
@@ -180,10 +204,10 @@ namespace CNORXZ
 	    virtual RangePtr extend(const RangePtr& r) const override final;
 
 	    /** Get local range. */
-	    Sptr<Range> local() const;
+	    Sptr<RangeI> local() const;
 
 	    /** Get range of the rank geometry. */
-	    Sptr<YRange> geom() const;
+	    Sptr<RangeK> geom() const;
 	    
 	    /** Get meta data for given lexicographic position.
 		@param pos Lexicographic position.
@@ -214,8 +238,8 @@ namespace CNORXZ
 	    */
 	    RRange(const Sptr<Range>& loc, const Sptr<YRange>& geom);
 	
-	    Sptr<Range> mLocal; /**< Local range of THIS rank. */
-	    Sptr<YRange> mGeom; /**< Rank geometry range. */
+	    Sptr<RangeI> mLocal; /**< Local range of THIS rank. */
+	    Sptr<RangeK> mGeom; /**< Rank geometry range. */
 	
 	};