  In this paper, we prove a K-theoretic wall-crossing formula for
$\epsilon$-stable quasimaps for all GIT targets in all genera. It recovers the
genus-0 K-theoretic toric mirror theorem by Givental-Tonita and the genus-0
mirror theorem for quantum K-theory with level structure by Ruan-Zhang. The
proofs are based on K-theoretic virtual localization on the master space
introduced by the second author in arXiv:1911.02745.
