Coactions and Fell bundles

Abstract

We show that if $\mathring{A}$ is a Fell bundle over a locally compact group $G$, then there is a natural coaction $\delta$ of $G$ on the Fell-bundle $C^{\ast }$-algebra $C^{\ast }(G,\mathring{A})$ such that if $\hat{\delta }$ is the dual action of $G$ on the crossed product $C^{\ast }(G,\mathring{A}){⋊}_{\delta }G$, then the full crossed product $(C^{\ast }(G,\mathring{A}){⋊}_{\delta }G){⋊}_{\hat{\delta }}G$ is canonically isomorphic to $C^*(G,Å) \otimes\KK(L^2(G))$. Hence the coaction $\delta$ is maximal.

39 Pages

References in corpus (1)

• Renault's Equivalence Theorem for Groupoid Crossed Products