Given a free and proper action of a groupoid on a Fell bundle (fibred over another groupoid), we give an equivalence between the semidirect-product and the generalized-fixed-point Fell bundles. This generalizes an earlier result where the action was by a group. As an application, we show that the Kumjian-Muhly Stabilization Theorem for Fell bundles over groupoids is essentially another form of crossed-product duality.

This presentation is based on joint work with Steve Kaliszewzki, John Quigg, and Dana Williams.