The Ordered K-Theory of C/*-Algebras¶Associated with Substitution Tilings

We consider the C ^*-algebra, A _T , constructed from a substitution tiling system which is primitive, aperiodic and satisfies the finite pattern condition. Such a C ^*-algebra has a unique trace. We show that this trace completely determines the order structure on the group K ₀(A _T ); a non-zero element in K ₀(A _T ) is positive if and only if its image under the map induced from the trace is positive. Received: 12 August 1999 / Accepted: 2 May 2000