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 -graph algebras.
Cite this article
Christian Bönicke, K-theory and homotopies of twists on ample groupoids. J. Noncommut. Geom. 15 (2021), no. 1, pp. 195–222DOI 10.4171/JNCG/399