K-theory and the connection index

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 K0 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 K0 contribute to the K-theory of the Iwahori C-algebra I(G). © 2012 London Mathematical Society.