Equivariant representable K-theory

Abstract

We interpret certain equivariant Kasparov groups as equivariant representable K-theory groups. We compute these groups via a classifying space and as K-theory groups of suitable sigma-C*-algebras. We also relate equivariant vector bundles to these sigma-C*-algebras and provide sufficient conditions for equivariant vector bundles to generate representable K-theory. Mostly we work in the generality of locally compact groupoids with Haar system.

Final version. Only minor corrections. 33 pages

References in corpus (2)

• Dualities in equivariant Kasparov theory
• Twisted K-theory of differentiable stacks

Cited by in corpus (16)

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• Equivariant K-theory, groupoids and proper actions
• Twisted equivariant K-theory, groupoids and proper actions
• Equivariant correspondences and the Borel-Bott-Weil theorem
• The Completion Theorem in twisted equivariant $K$-Theory for proper and discrete actions
• Twisted Geometric K-homology for Proper actions of discrete groups
• K-Theory for group C^*-algebras
• A categorical perspective on the Atiyah-Segal completion theorem in $\mathrm{KK}$-theory
• Structure and K-theory of crossed products by proper actions
• Nonlinearity, Proper Actions and Equivariant Stable Cohomotopy
• Baum-Connes and the Fourier-Mukai transform