  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.
