Equivariant completions of rings with reductive group action (Q1109096)

From author's summary: Let the connected reductive algebraic group G act on the affine variety X, over an algebraically closed field of characteristic zero. The largest G-rational submodule of the completion of the coordinate ring of X along the ideal of a closed orbit is an equivariant completion. If the orbit is a local complete intersection in X, and if H denotes its stabilizer, then it is shown that the equivariant completion is G-isomorphic to the equivariant completion of the induction from H to G of the symmetric algebra of a finite-dimensional H-module.