  We considered the lattice electroweak theory at realistic values of $\alpha$
and $\theta_W$ and for large values of the Higgs mass. We investigated
numerically the properties of topological objects that are identified with
quantum Nambu monopoles. We have found that the action density near the Nambu
monopole worldlines exceeds the density averaged over the lattice in the
physical region of the phase diagram. Moreover, their percolation probability
is found to be an order parameter for the transition between the symmetric and
the broken phases. Therefore, these monopoles indeed appear as real physical
objects. However, we have found that their density on the lattice increases
with increasing ultraviolet cutoff. Thus we conclude, that the conventional
lattice electroweak theory is not able to predict the density of Nambu
monopoles. This means that the description of Nambu monopole physics based on
the lattice Weinberg - Salam model with finite ultraviolet cutoff is
incomplete. We expect that the correct description may be obtained only within
the lattice theory that involves the description of TeV - scale physics.
