Degeneracy loci classes in K-theory - determinantal and Pfaffian formula

We prove a determinantal formula that describes the K-theoretic degeneracy loci classes for Grassmann bundles. We further prove Pfaffian formulas for symplectic and odd orthogonal Grassmann bundles. The former generalizes Damon-Kempf-Laksov's determinantal formula, and the latter generalize Pragacz-Kazarian's formulas for the Chow ring.