In this talk I will define the quantum K-theory for Nakajima quiver varieties and show its connection to representation theory of quantum groups on the example of the Grassmannian. In particular, the Baxter operator will be identified with operators of quantum multiplication by quantum tautological classes. Quantum tautological classes will also be constructed and an explicit universal combinatorial formula for them will be shown.

Based on a joint work with A.Smirnov and A.Zeitlin.