Combinatorics of K-theory via aK-theoretic Poirier–Reutenauer bialgebra

We use the -Knuth equivalence of Buch and Samuel (2015) to define a -theoretic analogue of the Poirier–Reutenauer Hopf algebra. As an application, we rederive the -theoretic Littlewood–Richardson rules of Thomas and Yong (2009, 2011) and of Buch and Samuel (2015).