Vexillary degeneracy loci classes in K-theory and algebraic cobordism

In this paper, we prove determinantal formulas for the K-theory classes of the structure sheaves of degeneracy loci associated to vexillary permutations in type A. As a consequence we obtain determinantal formulas for Lascoux-Schützenberger's double Grothendieck polynomials associated to vexillary permutations. We also prove a generalization of the formula in algebraic cobordism.