  We propose the notion of q-characters for finite-dimensional representations
of quantum affine algebras. It is motivated by our theory of deformed
W-algebras. We show that the q-characters give rise to a homomorphism from the
Grothendieck ring of representations of a quantum affine algebra to a
polynomial ring. We conjecture that the image of this homomorphism is equal to
the intersection of certain "screening operators". We also discuss the
connection between q-characters and Bethe Ansatz.
