  In this paper we introduce an intrinsic version of the classical induction of
representations for a subgroup $H$ of a (finite) group $G$, called here {\em
geometric induction}, which associates to any, not necessarily transitive,
$G$-set $X$ and any representation of the action groupoid $A(G,X)$ associated
to $G$ and $X$, a representation of the group $G$. We show that geometric
induction, applied to one dimensional characters of the action groupoid of a
suitable $G$-set $X$ affords a Gelfand Model for $G$ in the case where $G$ is
either the symmetric group or the projective general linear group of rank $2$.
