  We show that every finitely-generated non-amenable linear group over a field
of characteristic zero admits an ergodic action which is rigid in the sense of
Popa. If this group has trivial solvable radical, we prove that these actions
can be chosen to be free. Moreover, we give a positive answer to a question
raised by Ioana and Shalom concerning the existence of such a free action for
$\mathbb{F}_2\times\Z$. More generally, we show that for groups $\Gamma$
considered by Fernos in \cite{Fer}, e.g. Zariski-dense subgroups in
PSL$_n(\R)$, the product group $\Gamma\times \Z$ admit a free ergodic rigid
action. Also, we investigate how rigidity of an action behaves under
restriction and co-induction. In particular, we show that rigidity passes to
co-amenable subgroups.
