  In this note we describe a seemingly new approach to the complex
representation theory of the wreath product $G\wr S_d$ where $G$ is a finite
abelian group. The approach is motivated by an appropriate version of
Schur-Weyl duality. We construct a combinatorially defined groupoid in which
all endomorphism algebras are direct products of symmetric groups and prove
that the groupoid algebra is isomorphic to the group algebra of $G\wr S_d$.
This directly implies a classification of simple modules. As an application, we
get a Gelfand model for $G\wr S_d$ from the classical involutive Gelfand model
for the symmetric group. We describe the Schur-Weyl duality which motivates our
approach and relate it to various Schur-Weyl dualities in the literature.
Finally, we discuss an extension of these methods to all complex reflection
groups of type $G(\ell,k,d)$.
