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Patrias and Pylyavskyy introduced shifted Hecke insertion as an applicationof their theory of dual filtered graphs. We use shifted Hecke insertion toconstruct symmetric function representatives for the K-theory of the orthogonalGrassmannian. These representatives are closely related to the shiftedGrothendieck polynomials of Ikeda and Naruse. We then recover the K-theorystructure coefficients of Clifford-Thomas-Yong/Buch-Samuel by introducing ashifted K-theoretic Poirier-Reutenauer algebra. Our proofs depend on the theoryof shifted K-theoretic jeu de taquin and the weak K-Knuth relations.

Shifted Hecke insertion and the K-theory of OG(n,2n+1)