$\mathrm{K}$-theory and homotopies of twists on ample groupoids

Abstract

This paper investigates the K-theory of twisted groupoid C * -algebras. It is shown that a homotopy of twists on an ample groupoid satisfying the Baum-Connes conjecture with coefficients gives rise to an isomorphism between the K-theory groups of the respective twisted groupoid C * -algebras. The results are also interpreted in an inverse semigroup setting and applied to generalized Renault-Deaconu groupoids and P -graph algebras.2010 Mathematics Subject Classification. 46L80, 46L55. Key words and phrases. Twisted groupoid C * -algebra, K-theory. This research was partially supported by Deutsche Forschungsgemeinschaft (SFB 878).