when $x$ is a grassmannian, marian-oprea-pandharipande and toda constructed alternate compactifications of spaces of maps from curves to $x$. the construction has been generalized to a large class of git quotients $x=w//g$ by ciocan-fontanine-kim-maulik and many others. it is called the theory of $\epsilon$-stable quasimaps. in this talk, we will introduce permutation-equivariant k-theoretic epsilon-stable quasimap invariants and prove their wall-crossing formulae for all targets in all genera. the wall-crossing formulae generalize givental's k-theoretic toric mirror theorem in genus zero. in physics literature, these k-theoretic invariants are related to the $3d n = 2$ supersymmetric gauge theories studied by jockers-mayr, and the wall-crossing formulae can be interpreted as relations between invariants in the uv and the ir phases of the $3d$ gauge theory. it is based on joint work with yang zhou.