K-theoretic Gromov-Witten invariants are holomorphic Euler characteristicsof various interesting vector bundles over Kontsevich's moduli spaces ofstable maps.The problem of computing these invariants is well-motivated by examples offlag manifolds, where quantum K-theory turned out to be related toquantum groups and finite-difference versions of Toda lattices (prettymuch the same way as quantum cohomology theory of flag manifolds isrelated to semisimple Lie groups and differential Toda lattices).Although it seems natural to express K-theoretic Gromov-Witten invariantsin terms of the usual (cohomological) ones by means of the formula ofRiemann-Roch-Hirzebruch, there has been little success in […]