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We present a formulation of Double Field Theory with a Drinfeld double as extended spacetime. It makes Poisson-Lie T-duality (including abelian and non-abelian T-duality as special cases) manifest. This extends the scope of possible applications of the theory, which so far captured abelian T-duality only, considerably. The full massless bosonic subsector (NS/NS and R/R) of type II string theories is covered.

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