The set-up is this: Let $G$ be a finite group, and $H$ a subgroup. We are given an irreducible representation of $H, \rho: H\rightarrow GL_n(K)$ (I will notationally identify $\rho$ with its character). I want to decompose $Ind^G_H(\rho)$ into irreducibles. I am given character tables of both $G$ and $H$.

If $K$ were $\mathbb{C}$, Frobenius reciprocity (https://planetmath.org/FrobeniusReciprocity) will do the trick. However, I am in the modular case; meaning: $char(K)||H|$. I still have all the character tables, except now they are Brauer character tables for the correct characteristic.

Is there a method for decomposing $Ind^G_H(\rho)$ into irreducible (Brauer) characters?

Edit: I wanted to make clear that since in the modular case we don't have Maschke's theorem, the ``decomposition'' into irreducibles would be in the Grothendieck group of Brauer characters of $G$. (representations of $G$ wouldn't nec. be direct sums of irreducible representations)