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

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.