Grothendieck classes of quiver cycles as iterated residues

In the case of Dynkin quivers we establish a formula for the Grothendieck class of a quiver cycle as the iterated residue of a certain rational function, for which we provide an explicit combinatorial construction. Moreover, we utilize a new definition of the double stable Grothendieck polynomials due to Rimanyi and Szenes in terms of iterated residues to exhibit how the computation of quiver coefficients can be reduced to computing coefficients in Laurent expansions of certain rational functions.