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completion theorem

Journal of K-Theory (1)

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Equivariant K-theory, groupoids and proper actions
Jose Cantarero
Journal:

Journal of K-Theory / Volume 9 / Issue 3 / June 2012

Published online by Cambridge University Press:

21 November 2011, pp. 475-501

Print publication:

June 2012
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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 -CW-complexes. We also establish an analogue of the completion theorem of Atiyah and Segal. Some examples are discussed.