For a closed orientable surface
S, any map f : S→S whose n-th power is homotopic to the identity, is homotopic to
a homeomorphism g of S of order n. This famous theorem of Nielsen is known to fail
in general for aspherical manifolds. In this paper, for model aspherical manifolds M
associated to a finitely extendable set of data, we, however, present a weaker version
of Nielsen’s result. We show that any homotopically periodic self-map f
of M is homotopic to a fiber preserving homeomorphism g of M of finite
order (but the order of g is not necessarily equal to the homotopy period of
f).
