  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 introduce a
geometric method to overcome this restriction and 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 the
quasi-conformal blender, a local and stable mechanism/phenomenon introduced in
this paper, which encapsulates our method to prove stable local ergodicity by
providing quasi-conformal orbits with fine controlled geometry. The
quasi-conformal blender is developed in the context of pseudo-semigroup actions
of locally defined smooth diffeomorphisms. This allows for applications in
different settings, including for the smooth foliations of arbitrary
codimension.
