We define a new action of the symmetric group and its Hecke algebra on poly
nomial rings whose invariants are exactly the quasi-symmetric polynomials.
We interpret this construction in terms of a Demazure character Formula for
the irreducible polynomial modules of a degenerate quantum group. We use t
he action of the generic Hecke algebras to define quasi-symmetric and nonco
mmutative analogues of Hall-Littlewood functions. We show that these genera
lized functions share many combinatorial properties with the classical ones
.