  In this paper, we study stable ergodicity of the action of groups of
diffeomorphisms on smooth manifolds. The existence of such actions is known
only on one-dimensional manifolds. The aim of this paper is to overcome this
restriction and to give a method for constructing higher-dimensional examples.
In particular, we show that every closed manifold admits stably ergodic
finitely generated group actions by diffeomorphisms of class $C^{1+\alpha}$. We
also prove the stable ergodicity of certain algebraic actions including the
natural action of a generic pair of matrices near the identity on a sphere of
arbitrary dimension. These are consequences of a new local and stable
mechanism/phenomenon which we call quasi-conformal blender. This tool stably
provides quasi-conformal orbits and yields stable local ergodicity. The
quasi-conformal blender is developed in the context of pseudo-semigroup actions
of locally defined smooth diffeomorphisms which allows for applications in
several different settings.
