Szegő Kernel Asymptotics on Complete Strictly Pseudoconvex CR Manifolds

We prove a Bochner–Kodaira–Nakano formula and establish Szegő kernel expansions on complete strictly pseudoconvex CR manifolds with transversal CR R\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbb {R}$$\end{document}-action under certain natural geometric conditions. As a consequence we show that such manifolds are locally CR embeddable.