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

TL;DR

This paper proves the maximality of dual coactions on full cross-sectional C*-algebras of Fell bundles, extending exotic crossed-product functors and analyzing K-theory for Fell-bundles over K-amenable groups.

Contribution

It provides a simple proof of maximality of dual coactions and extends exotic crossed-product functors to Fell bundles and partial actions.

Findings

Maximality of dual coactions on full cross-sectional C*-algebras of Fell bundles.

Extension of exotic crossed-product functors to Fell bundles and partial actions.

Results on the K-theory of cross-sectional algebras over K-amenable groups.

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.