  We study nestohedra $P_B$ corresponding to building sets $B$. It is shown
that every flag nestohedron can be obtained from a cube by successive shavings
faces of codimension 2. We receive new Delzant geometric realization of flag
nestohedra. The main result of the paper is that Gal's conjecture holds for
every flag nestohedron. Moreover, we get the exact estimation of
$\gamma$-vectors of $n$-dimensional flag nestohedra:
$0\leq\gamma_i(P_B)\leq\gamma_i(Pe^n)$.
