Groupoid Crossed Products of Continuous-Trace C*-Algebras

Abstract

We show that if $(A,G,\alpha )$ is a groupoid dynamical system with $A$ continuous trace, then the crossed product $A{⋊}_{\alpha }G$ is Morita equivalent to the C*-algebra $C\ast (\underline{G},\underline{E})$ of a twist $\underline{E}$ over a groupoid $\underline{G}$ equivalent to $G$. This is a groupoid analogue of the well known result for the crossed product of a group acting on an elementary C*-algebra.

20 Pages, To appear in the Journal of Operator Theory