  We have investigated structure formation in the $\gamma$ gravity $f(R)$ model
with {\it N}-body simulations. The $\gamma$ gravity model is a proposal which,
unlike other viable $f(R)$ models, not only changes the gravitational dynamics,
but can in principle also have signatures at the background level that are
different from those obtained in $\Lambda$CDM (Cosmological constant, Cold Dark
Matter). The aim of this paper is to study the nonlinear regime of the model in
the case where, at late times, the background differs from $\Lambda$CDM. We
quantify the signatures produced on the power spectrum, the halo mass function,
and the density and velocity profiles. To appreciate the features of the model,
we have compared it to $\Lambda$CDM and the Hu-Sawicki $f(R)$ models. For the
considered set of parameters we find that the screening mechanism is
ineffective, which gives rise to deviations in the halo mass function that
disagree with observations. This does not rule out the model per se, but
requires choices of parameters such that $|f_{R0}|$ is much smaller, which
would imply that its cosmic expansion history cannot be distinguished from
$\Lambda$CDM at the background level.
