  For a finite group G one may consider the associated tower S_n[G] of wreath
product groups. Zelevinsky associates to such a tower a positive self-adjoint
Hopf algebra (PSH-algebra) R(G) as the infinite direct sum of the Grothendieck
groups of the categories of complex representations of these groups. In this
paper, we study the interaction via induction and restriction of the
PSH-algebras R(G) and R(H) for subgroups H of G. A class of Hopf modules over
PSH-algebras with a compatibility between the comultiplication and
multiplication involving the Hopf k^{th}-power map arise naturally and are
studied independently. We also give an explicit formula for the natural
PSH-algebra morphisms between R(H) and R(G) arising from induction and
restriction. In an appendix, we consider the more general family of restricted
wreath products, which are subgroups of wreath product groups analogous to the
subgroups G(m, p, n) of the wreath product cyclotomic complex reflection groups
G(m, 1, n).
