Equivariant embeddings of strongly pseudoconvex Cauchy-Riemann manifolds

Let X be a CR manifold with transversal, proper CR action of a Lie group G. We show that the quotient X/G is a complex space such that the quotient map is a CR map. Moreover the quotient is universal, i.e. every invariant CR map into a complex manifold factorizes uniquely over a holomorphic map on X/G. We then use this result and complex geometry to prove an embedding theorem for (non-compact) strongly pseudoconvex CR manifolds with transversal G (sic) S-1-action. The methods of the proof are applied to obtain a projective embedding theorem for compact CR manifolds.