K-Theory And Homotopies Of Twists On Ample Groupoids

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.