Billey-Type Formula for KL-Schubert Classes in Hyperbolic Cohomology

This paper studies the KL-Schubert classes defined by Kazhdan-Lusztig bases in $K$-theory and hyperbolic cohomology of flag varieties. We first establish Poincaré dualities of these classes. We then focus on Grassmannians, and establish the Billey-type formula for KL-Schubert classes in hyperbolic cohomology.