  A new version of double field theory (DFT) is derived for the exactly
solvable background of an in general left-right asymmetric WZW model in the
large level limit. This generalizes the original DFT that was derived via
expanding closed string field theory on a torus up to cubic order. The action
and gauge transformations are derived for fluctuations around the generalized
group manifold background up to cubic order, revealing the appearance of a
generalized Lie derivative and a corresponding C-bracket upon invoking a new
version of the strong constraint. In all these quantities a background
dependent covariant derivative appears reducing to the partial derivative for a
toroidal background. This approach sheds some new light on the conceptual
status of DFT, its background (in-)dependence and the up-lift of non-geometric
Scherk-Schwarz reductions.
