Let ${ \bf G}$ be a connected reductive group over $\bar{ \mathbb{ F}}_q$, the algebraically closure of $\mathbb{ F}_q$ (the finite field with $q=p^e$ elements), with the standard Frobenius map $F$. Let ${ \bf B}$ be an $F$-stable Borel subgroup. Let $\Bbbk$ be a field of characteristic $r\neq p$. In this paper, we completely determine the composition factors of the induced module $Ind_{ B}^{ G}{ tr}=\Bbbk{ G}\otimes_{ \Bbbk{ \bf B}}$ tr (here $\Bbbk{ H}$ is the group algebra of the group ${ H}$, and tr is the trivial $B$-module). In particular, we find a new family of infinite dimensional irreducible abstract representations of $G$.
Categories: math.RT