Rigidity for equivalence relations on homogeneous spaces

We study Popa's notion of rigidity for equivalence relations induced by actions on homogeneous spaces. For any lattices Gamma and Lambda in a semisimple Lie group G with finite center and no compact factors we prove that the action Gamma (sic) G/Lambda is rigid. If in addition G has property (T) then we derive that the von Neumann algebra L-infinity (G/Lambda) (sic) Gamma has property (T). We also show that if the stabilizer of any non-zero point in the Lie algebra of G under the adjoint action of G is amenable (e. g., if G = SL2(R)), then any ergodic subequivalence relation of the orbit equivalence relation of the action Gamma (sic) G/Lambda is either hyperfinite or rigid.