The coarse BaumConnes conjecture and groupoids
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To every discrete metric space with bounded geometry X we associate a groupoid G(X) for which the coarse assembly map for X is equivalent to the Baum-Connes assembly map for G(X) with coefficients in the C* -algebra L (X, K). We thus obtain a new proof of the fact that if X admits a uniform embedding into Hilbert space, the coarse assembly map is an isomorphism. If furthermore X is a discrete group with a translation-invariant metric, we show, using Higson's descent technique, that also satisfies the Novikov conjecture. This removes the finiteness condition in (Yu, Invent. Math. 139 (2000) 201-204). 2002 Elsevier Science Ltd. All rights reserved.