  In this paper, we first discuss the topological properties of projective
Stiefel manifolds, we compute their cohomology rings and classify their
cohomology endomorphisms; Then by embedding the flag manifold of a classical
Lie group into its corresponding infinite dimensional projective Stiefel
manifold(which is homotopic to the product of infinite dimensional complex
projective space $\mathbb{C}P^{\infty}$), we define the Schubert polynomials
and dual Schubert polynomials. Finally we discuss the property and the
computation of these polynomials.
