  The main theorem is that if K is a finite CW complex with finite fundamental
group G and universal cover homotopy equivalent to a product of spheres X, then
G acts smoothly and freely on X x S^n for any n greater than or equal to the
dimension of X. If the G-action on the universal cover of K is homologically
trivial then so is the action on X x S^n.
  Unlu and Yalcin recently showed that for every finite group G, there is a
finite CW complex K with fundamental group G which acts homologicially
trivially on the universal cover of K.
  Thus every finite group acts smoothly, freely, and homologically trivially on
a product of spheres.
