  We generalize the Poisson-Lie T-duality by making use of the structure of the
affine Poisson group which is the concept introduced some time ago in Poisson
geometry as a generalization of the Poisson-Lie group. We also introduce a new
notion of an affine quasi-Poisson group and show that it gives rise to a still
more general T-duality framework. We establish for a class of examples that
this new T-duality is compatible with the renormalization group flow.
