  An element of a Weyl group of classical type is skew if it is the left factor
in a reduced factorization of a Grassmannian element. The skew Grothendieck
polynomials are those which are indexed by skew elements of the Weyl group. We
define set-valued tableaux which are fillings of the associated skew Young
diagrams and use them to prove tableau formulas for the skew double
Grothendieck polynomials in all four classical Lie types. We deduce tableau
formulas for the Grassmannian Grothendieck polynomials and the K-theoretic
analogues of the (double mixed) skew Stanley functions in the respective Lie
types.
