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CR geometry and CR embeddings arise naturally in the study of proper holomorphic mappings between smoothly bounded domains in several complex variables.CR invariants of the boundaries of domains are used to tell whether two domains are biholomorphically equivalent.The main way of producing such invariants involves using the CR Cartan(or Chern-Moser)connection.We apply this connection(in `tractor form)to the problem of constructing invariants of CR embeddings between CR manifolds.This extends ideas that have been useful in producing invariants of conformal embeddings(such as generalized Willmore invariants)to the CR setting.