  We provide abelianizations of differentiable actions of finite groups on
smooth real manifolds. De Concini-Procesi wonderful models for (local) subspace
arrangements and a careful analysis of linear actions on real vector spaces are
at the core of our construction. In fact, we show that our abelianizations have
stabilizers isomorphic to elementary abelian 2-groups, a setting for which we
suggest the term digitalization. As our main examples, we discuss the resulting
digitalizations of the permutation actions of the symmetric group on real
linear and projective spaces.
