  We define the open string version of the nonlinear sigma model on doubled
geometry introduced by Hull and Reid-Edwards, and derive its boundary
conditions. These conditions include the restriction of D-branes to maximally
isotropic submanifolds as well as a compatibility condition with the Lie
algebra structure on the doubled space. We demonstrate a systematic method to
derive and classify D-branes from the boundary conditions, in terms of
embeddings both in the doubled geometry and in the physical target space. We
apply it to the doubled three-torus with constant H-flux and find D0-, D1-, and
D2-branes, which we verify transform consistently under T-dualities mapping the
system to f-, Q- and R-flux backgrounds.
