  We prove a formula for the push-forward class of Bott-Samelson resolutions in
the algebraic cobordism ring of the flag bundle. We specialise our formula to
connective K-theory providing a geometric interpretation to the double
beta-polynomials of Fomin and Kirillov by computing the fundamental classes of
Schubert varieties. As a corollary we obtain a Thom-Porteous formula
generalising those of the Chow ring and of the Grothendieck ring of vector
bundles.
