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

Hopf Modules in the Representation Theory of Wreath Products