  In this paper, we construct stable Bott--Samelson classes in the projective
limit of the algebraic cobordism rings of full flag varieties, upon an initial
choice of a reduced word in a given dimension. Each stable Bott--Samelson class
is represented by a bounded formal power series modulo symmetric functions in
positive degree. We make some explicit computations for those power series in
the case of infinitesimal cohomology. We also obtain a formula of the
restriction of Bott--Samelson classes to smaller flag varieties.
