SzegA kernel expansion and equivariant embedding of CR manifolds with circle action

Let X be a compact strongly pseudoconvex CR manifold with a transversal CR -action. In this paper, we establish the asymptotic expansion of SzegA kernels of positive Fourier components, and by using the asymptotics, we show that X can be equivariant CR embedded into some equipped with a simple -action. An equivariant embedding of quasi-regular Sasakian manifold is also derived.