2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/68591We 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.14 pages, 3 figures; substantial revision of Section 4, minor corrections elsewhere, to appear in IMRNAlgebraic GeometryGeometric Topology58A35; 57N80text