On Nuclearity of $C\ast$-algebras of Fell Bundles over Étale Groupoids

Abstract

We show the nuclearity of the reduced $C^{\ast }$-algebra of a Fell bundle over an étale amenable groupoid, whose fibers over the unit space are all nuclear. We introduce the (minimal) tensor product of a Fell bundle and a $C^{\ast }$-algebra in order to show the uniqueness of tensor product norms.