I wish to ask about good examples of new applications of Lusztig's theory of character sheaves (and subsequent development, but excluding generalized Springer theory) back to the theory of characters of $G(\mathbb{F}_q)$ for a connected reductive group $G$ over $\mathbb{F}_q$. Thank you in advance!
(This is not about why character sheaves are important; I already find them very important for $p$-adic groups and many other places.)
I mean, I've always tried to understand characters of $G(\mathbb{F}_q)$ in the language and spirit of character sheaves. But then my knowledge is just a small subset of what Lusztig covered in the orange book before character sheaves anyway.
