  We propose a categorification of the cyclotomic Hecke algebra in terms of the
equivariant K-theory of the framed matrix factorizations. The construction
generalizes the earlier construction of the authors for a categorification of
the finite Hecke algebra of type A.
  We also explain why our construction provides a faithful realization of the
Hecke algebras and discuss a geometric realization of the Jucys-Murphy
subalgebra.
