Extending our reduction construction in (S. Hu, Hamiltonian
symmetries and reduction in generalized geometry, Houston J. Math.,
to appear, math.DG/0509060, 2005.) to the Hamiltonian action of a
Poisson Lie group, we show that generalized Kähler reduction exists
even when only one generalized complex structure in the pair is
preserved by the group action. We show that the constructions in
string theory of the (geometrical) T-duality with H-fluxes for principle
bundles naturally arise as reductions of factorizable Poisson Lie
group actions. In particular, the groups involved may be non-abelian.