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arXiv · 1409.4332

Exotic crossed products and the Baum-Connes conjecture

Alcides Buss·Siegfried Echterhoff·Rufus Willett
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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.

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Alcides Buss, Siegfried Echterhoff, Rufus Willett. 2014-09-15. Exotic crossed products and the Baum-Connes conjecture. https://arxiv.org/abs/1409.4332

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