  For each integral dominant weight $\lambda$, we construct a twisted global
section functor $\Gamma^{\lambda}$ 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 $\Gamma^{\lambda}$ is
exact and faithful. This generalized the work of Frenkel and Gaitsgory in the
case when $\lambda=0$.
