  We prove that if a finite group $H$ has a generalized involution model, as
defined by Bump and Ginzburg, then the wreath product $H \wr S_n$ also has a
generalized involution model. This extends the work of Baddeley concerning
involution models for wreath products. As an application, we construct a
Gelfand model for wreath products of the form $A \wr S_n$ with $A$ abelian, and
give an alternate proof of a recent result due to Adin, Postnikov, and Roichman
describing a particularly elegant Gelfand model for the wreath product $\ZZ_r
\wr S_n$. We conclude by discussing some notable properties of this
representation and its decomposition into irreducible constituents, proving a
conjecture of Adin, Roichman, and Postnikov's.
