Let \(G\) be a finite group with a split \(BN\)-pair of characteristic \(p\) satisfying the commutator relations. Let \(k\) be a splitting field for all subgroups of \(G\) such that \(\text{char}(k)=\ell\neq p\). This paper is a continuation of the work begun by the authors [in J. Algebra 168, No. 1, 182-220 (1994; Zbl 0840.20034)]. The aim is to establish a parametrization of the simple \(kG\)-modules by the triples \((L,X,\phi)\) where \(L\subseteq G\) is a split Levi subgroup, \(X\) is a cuspidal simple \(kL\)-module and \(\phi\) is a simple module of the endomorphism algebra of the induced \(kG\)-module \(\text{Ind}^G_L(X)\). This parametrization generalizes the one established in characteristic 0 in the work of Howlett-Lehrer and Deligne-Lusztig. The results of this paper are applied to some series of classical groups such as unitary, symplectic and odd dimensional orthogonal groups.