  Let R a be countable ergodic equivalence relation of type II_1 on a standard
probability space (X,m). The group Out(R) of outer automorphisms of R consists
of all invertible Borel measure preserving maps of the space which map
R-classes to R-classes modulo those which preserve almost every R-class. We
analyze the group Out(R) for relations R generated by actions of higher rank
lattices, providing general conditions on finiteness and triviality of Out(R)
and explicitly computing this group for the standard actions. The method is
based on Zimmer's superrigidity for measurable cocycles, Ratner's theorem and
Gromov's Measure Equivalence construction.
