  A self-consistent construction of the overlap lattice Dirac operator coupled
to chiral chemical potential is proposed. With the help of the constructed
operator we compute electric current induced by a constant magnetic field
(Chiral Magnetic Effect). We find that the result disagrees with the one
predicted by anomaly-based arguments and comment on the origin of this
discrepancy. We demonstrate that a straightforward lattice calculation with a
constant magnetic field and a uniform chiral chemical potential in fact
corresponds to an infrared singularity in the dimensionally reduced
polarization tensor and hence yields the result which is extremely sensitive to
infrared regulators such as finite volume or finite temperature.
