# What is the Grothendieck group of characters of a finite group?

In Example 6.2 of Digne and Michel's textbook "Representations of Finite Groups of Lie Type", the use the notation $\mathcal{R}[{GL_n(\mathbb{F}_q)}]$, saying that $\mathcal{R}(H)$ denotes the Grothendieck group of characters for the finite group $H$.

What is this exactly? Does one construct a free commutative monoid on the set of characters of $H$, and then proceed to construct the Grothendieck group in the usual way?

• It is just the Abelian group of generalized characters of $H$. – alephalpha Apr 13 '18 at 7:49