Combinatorics of KK-theory via a KK-theoretic Poirier–Reutenauer bialgebra

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