Title: Formal group laws, T-equivariant oriented cohomology and
generalized Schubert calculus

In a series of papers Kostant and Kumar using the language of (nil-)Hecke
rings and the Goresky-Kottwitz-MacPherson moment map, produced an
algebraic model for the T-equivariant cohomology and K-theory of flag
varieties. In the present talk we discuss generalizations of this approach
to the context of an arbitrary equivariant algebraic oriented cohomology
theory (e.g. algebraic cobordism) in the sense of Levine-Morel. In
particular, we construct an algebraic model for the T-equivariant oriented
cohomology, we produce analogues of the Demazure and push-pull operators,
Bott-Samelson classes, push-forward formulas, root polynomials, etc. The
talk is based on recent joint papers with B. Calmes, C. Lenart, V. Petrov,
A. Savage, C. Zhong and others.