  We extend Bezrukavnikov and Finkelberg's description of the
G(\C[[t]])-equivariant derived category on the affine Grassmannian to the
twisted setting of Finkelberg and Lysenko. Our description is in terms of
coherent sheaves on the twisted dual Lie algebra. We also extend their
computation of the corresponding loop rotation equivariant derived category,
which is described in terms of Harish-Chandra bimodules for the twisted dual
Lie algebra. To carry this out, we have to find a substitute for the functor of
global equivariant cohomology. We describe such a functor, and show as in
Bezrukavnikov-Finkelberg that it is computed in terms of Kostant-Whittaker
reduction on the dual side.
