Integrability of dual coactions on Fell bundle C*-algebras

Abstract

We study integrability for coactions of locally compact groups. For abelian groups, this corresponds to integrability of the associated action of the Pontrjagin dual group. The theory of integrable group actions has been previously studied by Ruy Exel, Ralf Meyer and Marc Rieffel. Our goal is to study the close relationship between integrable group coactions and Fell bundles. As a main result, we prove that dual coactions on C*-algebras of Fell bundles are integrable, generalizing results by Ruy Exel for abelian groups.