Twisted global section functor for D-modules on affine Grassmannian

For each integral dominant weight $\lambda$, we construct a twisted global section functor ${\mathrm{\Gamma }}^{\lambda }$ from the category of critical twisted $D$-modules on affine Grassmannian to the category of $\lambda$-regular modules of affine Lie algebra at critical level. We proved that ${\mathrm{\Gamma }}^{\lambda }$ is exact and faithful. This generalized the work of Frenkel and Gaitsgory in the case when $\lambda =0$.