Quantum cohomology of flag variety G/B and homology ring of the affine Grassmanian of G are isomorphic if we localize both rings appropriately.This result was stated in a series of lectures by D. Peterson in 1997 at MIT, and a proof for G/P along the line of Peterson's lecture is available in a paper by T. Lam and M. Shimozono. The aim of this talk is to give a K-theoretic analogue of the isomorphism for G=SL(n). As is expected, the isomorphism admits a natural explanationin terms of integrable systems called relativistic Toda lattice due to Ruijsenaars. This is a joint work with S. Iwao and T. Maeno.