Groupoid Crossed Products of Continuous-Trace C*-Algebras

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 $C\ast (\underset{‾}{G},\underset{‾}{E})$ of a twist $\underset{‾}{E}$ over a groupoid $\underset{‾}{G}$ 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.