In this paper we prove an equivariant version of Hormanders embedding theor
em for Stein manifolds. More concretely, let G be a connected Lie group sit
ting in its complexification G(C) and D subset of or equal to G(C) a G x G-
invariant Stein domain. Under slight obstructions on D we construct a Hilbe
rt space H equipped with a unitary G x G-action and a holomorphic equivaria
nt closed embedding e: D --> H*\{0}.