  Let G denote a split simply connected almost simple p-adic group. The
classical example is the special linear group SL(n). We study the K-theory of
the unramified unitary principal series of G and prove that the rank of K_0 is
the connection index f(G). We relate this result to a recent refinement of the
Baum-Connes conjecture, and show explicitly how generators of K_0 contribute to
the K-theory of the Iwahori C*-algebra I(G).
