ON THE K-THEORY OF C-ALGEBRAS OF PRINCIPAL GROUPOIDS

We consider the K-theory of C*-algebras of principal r-discrete groupoids. We describe two basic situations in which three groupoids are related; they can very loosely be described as "factor groupoids" and "sub-groupoids." For each, we show that there is a six-term exact sequence of associated K-groups. We present examples which arise from dynamical systems and from problems in the study of the orbit structure of topological systems. We also obtain the usual Mayer-Vietoris sequence in topological K-theory as a corollary.