  We study Popa's notion of rigidity for equivalence relations induced by
actions on homogeneous spaces. For any lattices $\Gamma,\Lambda$ in a
semisimple Lie group $G$ with finite center and no compact factors we prove
that the action $\Gamma\curvearrowright G/\Lambda$ is rigid. If in addition $G$
has property (T) then we derive that the von Neumann algebra
$L^{\infty}(G/\Lambda)\rtimes\Gamma$ has property (T). We also show that if the
adjoint action of $G$ on the Lie algebra of $G$ - $\{0\}$ is amenable (e.g. if
$G=SL_2(\Bbb R)$), then any ergodic subequivalence relation of the orbit
equivalence relation of the action $\Gamma\curvearrowright G/\Lambda$ is either
hyperfinite or rigid.
