Abstract:

(This is a joint work with Martina Lanini and Rui Xiong.)
We prove that the structure algebra of a Bruhat moment graph of a finite real root system is a Hopf algebroid
(in the language of 2-monoidal categories) with respect to the Hecke and the Weyl actions. In particular, it
implies that the natural Hopf-algebra structure on the algebraic oriented cohomology A(G) of Levine-Morel of
a split semi-simple linear algebraic group G can be lifted to a `bi-Hopf' structure on the T-equivariant
algebraic oriented cohomology of the complete flag variety A_T(G/B). Observe that the Hopf-structure (and the
induced comodule-structure) was used by Petrov-Semenov to obtain new restrictions for motivic-decomposition types
of twisted flag varieties. We also discuss various applications of this result to generalized Schubert calculus,
to Coxeter groups and finite real root systems, e.g., we compute `CH(I_2(p))’, where $p$ is an odd prime.