  We consider a scattering theory for convolution operators on
$\mathcal{H}=\ell^2(\mathbb{Z}^d; \mathbb{C}^n)$ perturbed with a long-range
potential $V:\mathbb{Z}^d\to\mathbb{R}^n$. One of the motivating examples is
discrete Schr\"odinger operators on $\mathbb{Z}^d$-periodic graphs. We
construct time-independent modifiers, so-called Isozaki-Kitada modifiers, and
we prove that the modified wave operators with the above-mentioned
Isozaki-Kitada modifiers exist and that they are complete.
