  We prove a relative version of Kontsevich's formality theorem. This theorem
involves a manifold M and a submanifold C and reduces to Kontsevich's theorem
if C=M. It states that the DGLA of multivector fields on an infinitesimal
neighbourhood of C is L-infinity-quasiisomorphic to the DGLA of
multidifferential operators acting on sections of the exterior algebra of the
conormal bundle. Applications to the deformation quantisation of coisotropic
submanifolds are given. The proof uses a duality transformation to reduce the
theorem to a version of Kontsevich's theorem for supermanifolds, which we also
discuss. In physical language, the result states that there is a duality
between the Poisson sigma model on a manifold with a D-brane and the Poisson
sigma model on a supermanifold without branes (or, more properly, with a brane
which extends over the whole supermanifold).
