The Novikov conjecture for linear groups
Publications Mathématiques de l'IHÉS, Volume 101 (2005), pp. 243-268.

Let K be a field. We show that every countable subgroup of GL (n,K) is uniformly embeddable in a Hilbert space. This implies that Novikov’s higher signature conjecture holds for these groups. We also show that every countable subgroup of GL (2,K) admits a proper, affine isometric action on a Hilbert space. This implies that the Baum-Connes conjecture holds for these groups. Finally, we show that every subgroup of GL (n,K) is exact, in the sense of C * -algebra theory.

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     title = {The {Novikov} conjecture for linear groups},
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Guentner, Erik; Higson, Nigel; Weinberger, Shmuel. The Novikov conjecture for linear groups. Publications Mathématiques de l'IHÉS, Volume 101 (2005), pp. 243-268. doi : 10.1007/s10240-005-0030-5. http://www.numdam.org/articles/10.1007/s10240-005-0030-5/

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