  (Bi)modules, morphisms and reduction of star-products are studied in a
framework of multidifferential operators along maps: morphisms deform Poisson
maps and representations on functions spaces deform coisotropic maps. If a
star-product is representable on a coisotropic submanifold, is is equivalent to
a star-product for which the vanishing ideal is a left ideal. If the reduced
phase space exists, a star-product with suitable Deligne class is representable
and the reduced algebra is the commutant of this module (hence a bimodule).
Obstructions to representability to third order are related to the
Atiyah-Molino class of the foliation of the coisotropic submanifold, and the
same kind of obstructions occurs for the quantisation of a Poisson map between
symplectic manifolds. For vanishing Atiyah-Molino class, the representation and
morphism problem is solvable.
