Abstract

We study the C * algebras associated with upper semicontinuous Fell bundles over secondcountable Hausdorff groupoids. Based on ideas going back to the Packer–Raeburn ‘stabilization trick’, we construct from each such bundle a groupoid dynamical system whose associated Fell bundle is equivalent to the original bundle. The upshot is that the full and reduced C * algebras of any saturated upper semicontinuous Fell bundle are stably isomorphic to the full and reduced crossed products of an associated dynamical system. We apply our results to describe the lattice of ideals of the C * algebra of a continuous Fell bundle by applying Renault's results about the ideals of the C * algebras of groupoid crossed products. In particular, we discuss simplicity of the Fellbundle C * algebra of a bundle over G in terms of an action, described by Ionescu and Williams, of G on the primitiveideal space of the C * algebra of the part of the bundle sitting over the unit space. We finish with some applications to twisted kgraph algebras, where the components of our results become more concrete.