Dressing cosets

An account of the Poisson-Lie T-duality is presented for the case when the action of the duality group on a target is not free. At the same time a generalization of the picture is given when the duality group does not even act on σ-model targets but only on their phase spaces. The outcome is a huge class of dualizable targets generically having no local isometries or Poisson-Lie symmetries whatsoever.