MAPS BETWEEN P-COMPLETED CLASSIFYING-SPACES .2.

We investigate maps between p-completed classifying spaces of compact connected Lie groups. Let G and G' be two connected compact Lie groups. For a space X, let X(p) be a p-completion of X. If p does not divide the order of the Weyl group of G, we give descriptions of the set of homotopy classes [(BG)p, (BG')p] in terms of K-theory and in terms of "admissible" maps of Adams and Mahmud.