Fell bundles and imprimitivity theorems: towards a universal generalized fixed point algebra

TL;DR

This paper extends Morita equivalence results for crossed products and fixed-point algebras using Fell bundles, providing a universal approach with several applications in operator algebra theory.

Contribution

It introduces a universal fixed-point algebra framework that generalizes Rieffel's Morita equivalence for proper saturated actions, connecting full and reduced crossed products.

Findings

Morita equivalence between reduced crossed product and fixed-point algebra as a quotient

Application to Fell bundles over groups

Connections to C*-bundles

Abstract

We apply the One-Sided Action Theorem from the first paper in this series to prove that Rieffel's Morita equivalence between the reduced crossed product by a proper saturated action and the generalized fixed-point algebra is a quotient of a Morita equivalence between the full crossed product and a "universal" fixed-point algebra. We give several applications, to Fell bundles over groups, reduced crossed products as fixed-point algebras, and C*-bundles.