We introduce a new method for studying the Baum-Connes conjecture, which we call the direct splitting method. The method can simplify and clarify proofs of some of the known cases of the conjecture. In a separate paper, with J. Brodzki, E. Guentner and N. Higson, a similar idea will be used to give a finite-dimensional proof of the Baum-Connes conjecture for groups which act properly and co-compactly on a finite-dimensional CAT(0)-cubical space.
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