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Twisted K-theory for actions of Lie groupoids and its completion theorem

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Abstract

In this paper we define twisted equivariant K-theory for actions of Lie groupoids. For a Bredon-compatible Lie groupoid \({\mathcal{G}}\), we show that this defines a periodic cohomology theory on the category of finite \({\mathcal{G}}\)–CW-complexes with \({\mathcal{G}}\)-stable projective bundles by comparing with a suitable representable cohomology theory. A classification of these bundles is shown. We also obtain a completion theorem and apply these results to proper actions of groups.

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  1. Facultat de Ciències, Edifici C, Universitat Autònoma de Barcelona, Centre de Recerca Matemàtica, 08193, Bellaterra, Spain

    Jose Cantarero

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  1. Jose Cantarero
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Cantarero, J. Twisted K-theory for actions of Lie groupoids and its completion theorem. Math. Z. 268, 559–583 (2011). https://doi.org/10.1007/s00209-010-0683-8

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  • DOI: https://doi.org/10.1007/s00209-010-0683-8

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