Remarks on modular representations of finite groups of Lie type in non-defining characteristic

Let $G$ be a finite group of Lie type and $\mathrm{\ell }$ be a prime which is not equal to the defining characteristic of $G$. In this note we discuss some open problems concerning the $\mathrm{\ell }$-modular irreducible representations of $G$. We also establish a strengthening of the results in [13] on the classification of the $\mathrm{\ell }$-modular principal series representations of $G$.