I will define the two Hecke actions on the dual of the formal affine
Demazure algebra. Then I will define the push-pull operators of the
oriented cohomology and define perfect pairings on the equivariant
cohomology of complete and partial flag varieties. If time permits, I
will talk about a parallel construction which gives the formal affine
Hecke algebra.

In this talk I will introduce the definition of formal affine Demazure
algebra and sketch the proof of the structure theorem. Taking its
dual, we get the algebraic replacement of $T$-equivariant oriented
cohomology of complete flag variety. I will also mention the proof of
the generalized Borel Isomorphism.

I will introduce the concept of oriented cohomology in the sense of
Levine and Morel, and the work of Kostant and Kumar on algebraic
construction of singular cohomology and Grothendieck group of flag
varieties. Then I will introduce the formal group algebra of
Calmes-Petrov-Zainoulline, which is the algebraic replacement of
$T$-equivariant oriented cohomology of a point.