  We rewrite the recently derived cubic action of Double Field Theory on group
manifolds [arXiv:1410.6374] in terms of a generalized metric and extrapolate it
to all orders in the fields. For the resulting action, we derive the field
equations and state them in terms of a generalized curvature scalar and a
generalized Ricci tensor. Compared to the generalized metric formulation of DFT
derived from tori, all these quantities receive additional contributions
related to the non-trivial background. It is shown that the action is invariant
under its generalized diffeomorphisms and 2D-diffeomorphisms. Imposing
additional constraints relating the background and fluctuations around it, the
precise relation between the proposed generalized metric formulation of
DFT${}_\mathrm{WZW}$ and of original DFT from tori is clarified. Furthermore we
show how to relate DFT${}_\mathrm{WZW}$ of the WZW background with the flux
formulation of original DFT.
