Averaging formula for Nielsen numbers

We prove that the averaging formula for Nielsen numbers holds for continuous maps on infra-nilmanifolds: Let M be an infra-nilmanifold and f : M -> M be a continuous map. Suppose M-K is a regular covering of M which is a compact nilmanifold with pi(1)(M-K) = K. Assume that f(*)(K) subset of K. Then f has a lifting f : MK MK on MK. We prove a question raised by McCord, which is for any alpha epsilon pi(1)(M) with p(Fix((alpha f) over bar)) an essential fixed point class, fix(T alpha phi) = 1. As a consequence, we obtain the following averaging formula for Nielsen numbers N(f) = 1 [pi 1(M) : K] Sigma alpha epsilon pi 1 (M)/K N ((a) over bar (f) over bar).