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## Operator $K$-Theory for groups which act on Hilbert space

### Nigel Higson and Gennadi Kasparov

**Abstract.**
Let $G$ be a countable discrete group which acts isometrically
and metrically properly on an infinite-dimensional Euclidean space.
We calculate the
$K$-theory groups of the $C^{*}$-algebras $C^{*}_{\max }(G)$ and $C^{*}_{
\smash{\text{red}}}(G)$. Our
result is in accordance with the Baum-Connes conjecture.

*Copyright 1997 American Mathematical Society*

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#### Article Info

- ERA Amer. Math. Soc.
**03** (1997), pp. 131-142
- Publisher Identifier: S 1079-6762(97)00037-1
- 1991
*Mathematics Subject Classification*. Primary 46L20
*Key words and phrases*. Baum-Connes conjecture, $C^{*}$-algebras,
$K$-theory
- Received by the editors October 25, 1997
- Posted on December 19, 1997
- Communicated by Masamichi Takesaki
- Comments (When Available)

**Nigel Higson**

Department of Mathematics, Pennsylvania State University,
University Park, PA 16802

*E-mail address:* `higson@math.psu.edu`

**Gennadi Kasparov**

Institut de Mathématiques de Luminy, CNRS-Luminy-Case 930, 163 Avenue
de Luminy 13288, Marseille Cedex 9, France

*E-mail address:* `kasparov@iml.univ-mrs.fr`

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