  We give a new construction of the Bott-Samelson variety $Z$ as the closure of
a $B$-orbit in a product of flag varieties $(G/B)^l$. This also gives an
embedding of the projective coordinate ring of the variety into the function
ring of a Borel subgroup: $\CC[Z] \subset \CC[B]$.
  In the case of the general linear group $G = GL(n)$, this identifies $Z$ as a
configuration variety of multiple flags subject to certain inclusion
conditions, closely related to the the matrix factorizations of Berenstein,
Fomin and Zelevinsky. As an application, we give a geometric proof of the
theorem of Kraskiewicz and Pragacz that Schubert polynomials are characters of
Schubert modules.
  Our work leads on the one hand to a Demazure character formula for Schubert
polynomials and other generalized Schur functions, and on the other hand to a
Standard Monomial Theory for Bott-Samelson varieties.
