K-theoretic tableau combinatorics

I will discuss a K-theoretic version of jeu de taquin, developed by Alex Yong and me in arxiv:0705.2915. We use the K-theoretic jeu de taquin to provide a combinatorial formula for the structure constants of the K-theory ring of the Grassmannian of k-planes in n-space. Other combinatorial formulas for the structure constants are already known; our formula has the attractive feature that it admits a natural conjectural extension to other minuscule types.