Smooth Schubert varieties and generalized Schubert polynomials in algebraic cobordism of Grassmannians

We provide several ingredients towards a generalization of the Littlewood- Richardson rule from Chow groups to algebraic cobordism. In particular, we prove a simple product formula for multiplying classes of smooth Schubert varieties with any Bott-Samelson class in algebraic cobordism of Grassmannians. We also establish some results for generalized Schubert polynomials for hyperbolic formal group laws.