2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/64609We construct a moduli space of stable projective pairs with a nontrivial action of a connected reductive group. These stable reductive pairs are higher-dimensional analogs of stable n-pointed curves and generalize to the non-commutative case a functorial compactification of moduli of abelian varieties, and of toric pairs. We prove that, confirming a prediction of log Minimal Program, stable reductive pairs have semi log canonical singularities. Final version, to appear in Advances of Math.26 pagesAlgebraic GeometryRepresentation Theory14D22; 20G05; 14M25text