  We study the action of the formal affine Hecke algebra on the formal group
algebra, and show that the the formal affine Hecke algebra has a basis indexed
by the Weyl group as a module over the formal group algebra. We also define a
concept called the normal formal group law, which we use to simplify the
relations of the generators of the formal affine Demazure algebra and the
formal affine Hecke algebra.
