  Let $\Gamma$ be a weakly irreducible higher rank lattice. In this paper, we
will prove various rigidity results for the $\Gamma$-action following a
philosophy of the Zimmer program. We provide new rigidity results including
local and global rigidity of the $\Gamma$-action when $\Gamma$ does not have
Property (T). The new ingredient is a dynamical cocycle super-rigidity theorem.
It can be thought of as the generalization of Zimmer's cocycle super-rigidity
theorem since it provides almost the same consequences dynamically and
algebraically. This allows us to derive various our rigidity results using
dynamical super-rigidity instead of Zimmer's cocycle super-rigidity theorem.
