Let G be an algebraic group and U be its maximal unipotent subgroup. In this talk, we will explore the global sections of chiral differential operators on the base affine space G/U, with a focus on introducing lifting formulas that transform functions on the cotangent bundle into global sections. A notable aspect of this framework is the mysterious Weyl group action, known as the Gelfand-Graev action, on the ring of differential operators on G/U. This action arises through algebra automorphisms rather than the natural geometric action of the Weyl group on the variety G/U. If time permits, we will also examine its extension to the realm of chiral differential operators.