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.