Let \(F\) be a non-Archimedean locally compact field of residue characteristic \(p\) and \( R\) be an algebraically closed field of characteristic \(l\) different from \(p.\) Let \(\mathbf G\) be the group \(\mathrm{GL}_n , n \geq 1, \) over \(F\) or one of its inner forms. The authors classify the unramified irreducible smooth \(R\)-representations of \({\mathbf G}(F).\) More precisely, they are those representations that are irreducibly induced from an unramified character of a Levi subgroup. It is deduced that any smooth irreducible unramified \(\bar F_l\)-representation of \({\mathbf G}(F)\) can be lifted to \(\bar {\mathbb Q}_l ,\) which proves a conjecture by Vignéras.