  The standard realization of the Hecke algebra on classical holomorphic cusp
forms and the corresponding period polynomials is well known. In this article
we consider a nonstandard realization of the Hecke algebra on Maass cusp forms
for the Hecke congruence subgroups Gamma_0(n). We show that the vector valued
period functions derived recently by Hilgert, Mayer and Movasati as special
eigenfunctions of the transfer operator for Gamma_0(n) are indeed related to
the Maass cusp forms for these groups. This leads also to a simple
interpretation of the ``Hecke like'' operators of these authors in terms of the
aforementioned non standard realization of the Hecke algebra on the space of
vector valued period functions.
