Actions of homeomorphism groups of manifolds admitting a nontrivial finite free action

In this paper, we study the action of Homeo₀ (M), the identity component of the group of homeomorphisms of an n-dimensional manifold M with an F_p-free action, on another manifold N of dimension n+k < 2n. We prove that if M is not an F_p-homology sphere, then N≅M×K for a homology manifold K such that the action of Homeo₀ (M) on M is standard and on K is trivial. In particular, for M = S_n a sphere, any nontrivial action is a generalization of the "coning-off" construction.