  We prove that if a countable discrete group $\Gamma$ is {\it w-rigid}, i.e.
it contains an infinite normal subgroup $H$ with the relative property (T)
(e.g. $\Gamma= SL(2,\Bbb Z) \ltimes \Bbb Z^2$, or $\Gamma = H \times H'$ with
$H$ an infinite Kazhdan group and $H'$ arbitrary), and $\Cal V$ is a closed
subgroup of the group of unitaries of a finite von Neumann algebra (e.g. $\Cal
V$ countable discrete, or separable compact), then any $\Cal V$-valued
measurable cocycle for a measure preserving action $\Gamma \curvearrowright X$
of $\Gamma$ on a probability space $(X,\mu)$ which is weak mixing on $H$ and
{\it s-malleable} (e.g. the Bernoulli action $\Gamma \curvearrowright
[0,1]^\Gamma$) is cohomologous to a group morphism of $\Gamma$ into $\Cal V$.
We use the case $\Cal V$ discrete of this result to prove that if in addition
$\Gamma$ has no non-trivial finite normal subgroups then any orbit equivalence
between $\Gamma \curvearrowright X$ and a free ergodic measure preserving
action of a countable group $\Lambda$ is implemented by a conjugacy of the
actions, with respect to some group isomorphism $\Gamma \simeq \Lambda$.
