GIT quotients of vector spaces by tori produce toric Deligne-Mumford stacks. Crossing a wall in the space of GIT stability conditions change the geometry of these DM stacks. It is known, that Gromov-Witten theories of the toric stacks obtained by such wall crossings are related. In the talk I will
outline one approach to relate K-theoretic quasimap invariants of the corresponding toric stacks based on interpolation problems for elliptic cohomology classes of the stacks.