  The symmetric Grothendieck polynomials generalize Schur polynomials and are
Schur-positive by degree. Combinatorially this is manifested as the
generalization of semistandard Young tableaux by set-valued tableaux. We define
a (weak) symmetric $P$-Grothendieck polynomial which generalizes $P$-Schur
polynomials in the same way. Combinatorially this is manifested as the
generalization of shifted semistandard Young tableaux by a new type of tableaux
which we call shifted multiset tableaux.
