Coactions and Fell bundles

Abstract

We show that if $à $ is a Fell bundle over a locally compact group $G$, then there is a natural coaction $δ$ of $G$ on the Fell-bundle $C^*$-algebra $C^*(G,à )$ such that if $\hatδ$ is the dual action of $G$ on the crossed product $C^*(G,à ) \rtimes_δ G$, then the full crossed product $(C^*(G,à ) \rtimes_δG)\rtimes_{\hatδ}G$ is canonically isomorphic to $C^*(G,à ) \otimes\KK(L^2(G))$. Hence the coaction $δ$ is maximal.

39 Pages