  We investigate a quantization problem which asks for the construction of an
algebra for relative elliptic problems of pseudodifferential type associated to
smooth embeddings. Specifically, we study the problem for embeddings in the
category of compact manifolds with corners. The construction of a calculus for
elliptic problems is achieved using the theory of Fourier integral operators on
Lie groupoids. We show that our calculus is closed under composition and
furnishes a so-called noncommutative completion of the given embedding. A
representation of the algebra is defined and the continuity of the operators in
the algebra on suitable Sobolev spaces is established.
