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We present a proof of a Littlewood–Richardson rule for the  K -theory of odd orthogonal Grassmannians OG( n ,2 n +1), as conjectured by Thomas–Yong (2009). Specifically, we prove that rectification using the  jeu de taquin  for increasing shifted tableaux introduced there, is well-defined and gives rise to an associative product. Recently, Buch–Ravikumar (2012) proved a Pieri rule for OG( n ,2 n +1) that confirms a special case of the conjecture. Together, these results imply the aforementioned conjecture.

K -theoretic Schubert calculus for OG( n ,2 n +1) and jeu de taquin for shifted increasing tableaux