  We construct central elements in a completion of the quantum affine algebra
at the critical level c=-g from the universal R-matrix (g being the dual
Coxeter number of the corresponding simple Lie algebra), using the method of
Reshetikhin and Semenov-Tian-Shansky. This construction defines an action of
the Grothendieck algebra of the category of finite-dimensional representations
of the quantum affine algebra on any module over this algebra from category O
with c=-g. We explain the connection between the central elements and transfer
matrices in statistical mechanics. In the quasiclassical approximation this
connection was explained by Feigin, E.Frenkel, and Reshetikhin in hep-th
9402022, and it was mentioned that one could generalize it to the quantum case
to get Bethe vectors for transfer matrices. Using this connection, we prove
that the central elements
  (for all finite dimensional representations) applied to the highest weight
vector of a generic Verma module at the critical level generate the whole space
of singular vectors in this module. We also compute the first term of the
quasiclassical expansion of the central elements near q=1, and show that it
always gives the Sugawara current with a certain coefficient.
