  We 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.
