  We show that the Gelfand character $ \chi_G$ of a finite group $G $ (i.e. the
sum of all irreducible complex characters
  of $G$ ) may be realized as a `` twisted trace'' $ g \mapsto Tr( \rho_g \circ
T) $ for a suitable involutive linear automorphism $T$ of $L^2(G)$, where
$(L^2(G), \rho)$ is the right regular representation of $G$. Moreover, we prove
that under certain hypotheses $T(f)= f \circ L \;\; (f \in L^2(G)), $ where $ L
$ is an involutive antiautomorphism of $ G.$ The natural representation $\tau$
of $G$ associated to the natural $L$-conjugacy action of $G$ in the fixed point
set $Fix_G(L)$ of $L$ turns out to be a Gelfand Model for $G$ in some cases. We
show that $(L^2(Fix_G(L)), \tau) $ fails to be a Gelfand Model if $G$ admits
non trivial central involutions.
