The main theorem here is the K-theoretic analogue of the
cohomological `stable double component formula' for quiver
polynomials in [Knutson-Miller-Shimozono 2003]. This
K-theoretic version is still in terms of lacing diagrams,
but nonminimal diagrams contribute terms of higher degree.
The motivating consequence is a conjecture of Anders Buch on the
sign-alternation of the coefficients appearing in his
expansion of quiver K-polynomials in terms of stable
Grothendieck polynomials [Duke Math. J., 2002].
(Simultaneously and independently, Buch has obtained a
different proof of his conjecture.)