Measuring the size of the coincidence set

Let Sm be a m-sphere (or, more generally, a homology m-sphere), Y a k-dimensional CW-complex and f :Sm→Y a continuous map. Let G be a finite group which acts freely on Sm. Suppose that H⊂G is a nontrivial normal cyclic subgroup of a prime order. We estimate the cohomological dimension of the set A(f,H,G) of (H,G)-coincidence points of f.