Maximality of dual coactions on sectional C*-algebras of Fell bundles and applications

Abstract

In this paper we give a simple proof of the maximality of dual coactions on full cross-sectional C*-algebras of Fell bundles over locally compact groups. As applications we extend certain exotic crossed-product functors in the sense of Baum, Guentner and Willett to the category of Fell bundles and the category of partial actions and we obtain results about the K-theory of (exotic) cross-sectional algebras of Fell-bundles over K-amenable groups. As a bonus, we give a characterisation of maximal coactions of discrete groups in terms of maximal tensor products.