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Let $G$ be a linear semisimple algebraic group and $B$ its Borel subgroup.Let $T\subset B$ be the maximal torus. We study the inductive construction ofBott-Samelson varieties to obtain recursive formulas for the twisted motivicChern classes of Schubert cells in $G/B$. To this end we introduce two familiesof operators acting on the equivariant K-theory $K_T(G/B)[y]$, the right andleft Demazure-Lusztig operators depending on a parameter. The twisted motivicChern classes coincide (up to normalization) with the K-theoretic stableenvelopes. Our results imply wall-crossing formulas for a change of weightchamber and slope parameters. The right and left operators generate a twisteddouble Hecke algebra. We show that in the type A this algebra acts on theLaurent polynomials. This action is a natural lift of the action on$K_T(G/B)[y]$ with respect to the Kirwan map. We show that the left and righttwisted Demazure-Lusztig operators provide a recursion for twisted motivicChern classes of matrix Schubert varieties.

Hecke algebra action on twisted motivic Chern classes and K-theoretic stable envelopes