On the K-theory of the stable C⁎-algebras from substitution tilings

We describe a method to compute the K-theory of the C⁎-algebra arising from the stable equivalence relation in the Smale space associated to a substitution tiling, and give detailed computations for one- and two-dimensional examples. We prove that for one-dimensional tilings the group K0 is always torsion free and give an example of a two-dimensional tiling such that K0 has torsion.