Exotic crossed products and the Baum-Connes conjecture
Abstract
We study general properties of exotic crossed-product functors and characterise those which extend to functors on equivariant C*-algebra categories based on correspondences. We show that every such functor allows the construction of a descent in KK-theory and we use this to show that all crossed products by correspondence functors of K-amenable groups are KK-equivalent. We also show that for second countable groups the minimal exact Morita compatible crossed-product functor used in the new formulation of the Baum-Connes conjecture by Baum, Guentner and Willett extends to correspondences when restricted to separable G-C*-algebras. It therefore allows a descent in KK-theory for separable systems.
Keywords
Cite
@article{arxiv.1409.4332,
title = {Exotic crossed products and the Baum-Connes conjecture},
author = {Alcides Buss and Siegfried Echterhoff and Rufus Willett},
journal= {arXiv preprint arXiv:1409.4332},
year = {2015}
}
Comments
New version has additional material on duality, and minor corrections