An excision theorem for the K-theory of C*-algebras, with applications to groupoid C*-algebras

We discuss the relative K-theory for a C*-algebra A, together with a C*-sub-algebra A' subset of A. The relative group is denoted Ki(A'; A), i = 0,1, and is due to Karoubi. We present a situation where two pairs A' subset of A and B' subset of B are related so that there is a natural isomorphism between their respective relative K-theories. We also discuss applications to the case where A and B are C*-algebras of a pair of locally compact, Hausdorff topological groupoids, with Haar systems.