  We introduce the most general to date version of the permutation-equivariant
quantum K-theory, and express its total descendant potential in terms of
cohomological Gromov-Witten invariants. This is the higher-genus analogue of
adelic characterization from the paper [7] by Givental-Tonita, and is based on
the application of Kawasaki's Riemann-Roch formula to moduli spaces of stable
maps.
