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

Cubical realizations of flag nestohedra and Gal's conjecture