  Fulton's universal Schubert polynomials give cohomology formulas for a class
of degeneracy loci, which generalize Schubert varieties. The K-theoretic quiver
formula of Buch expresses the structure sheaves of these loci as integral
linear combinations of products of stable Grothendieck polynomials. We prove an
explicit combinatorial formula for the coefficients, which shows that they have
alternating signs. Our result is applied to obtain new expansions for the
Grothendieck polynomials of Lascoux and Sch\"utzenberger.

Combinatorics;Algebraic Geometry