Equivariant K-theory, groupoids and proper actions

Abstract

In this paper we define complex equivariant K-theory for actions of Lie groupoids using finite-dimensional vector bundles. For a Bredon-compatible Lie groupoid, this defines a periodic cohomology theory on the category of finite equivariant CW-complexes. We also establish an analogue of the completion theorem of Atiyah and Segal. Some examples are discussed.

26 pages, v3 Correction to some lemmas and definitions in section 4. Added a page at the end of section 3. Other minor corrections

References in corpus (6)

• Twisted K-theory and loop group representations
• Loop groups and twisted K-theory I
• Homotopy Theory of Orbispaces
• Equivariant representable K-theory
• Thom Prospectra for Loopgroup representations
• Twisted equivariant K-theory for proper actions of discrete groups

Cited by in corpus (1)

• On minimal finite quotients of outer automorphism groups of free groups