  Averaging certain class of quasiperiodic monotone operators can be simplified
to the periodic homogenization setting by mapping the original quasiperiodic
structure onto a periodic structure in a higher dimensional space using cut-and
projection method. We characterize cut-and-projection convergence limit of the
nonlinear monotone partial differential operator $-\mathrm{div} \;
\sigma\left({\bf x},\frac{{\bf R}{\bf x}}{\eta}, \nabla u_\eta\right)$ for a
bounded sequence $u_\eta$ in $W^{1,p}_0(\Omega)$, where $1<p < \infty$,
$\Omega$ is a bounded open subset in $R^n$ with Lipschitz boundary. We identify
the homogenized problem with a local equation defined on the hyperplane in the
higher-dimensional space. A new corrector result is established.
