  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 $G$.
