Since Geordie Williamson showed that the exceptional primes for an algebraic group grow at least exponentially with the rank, the problem of calculating simple characters seems to be less approachable than ever before. In the talk I will give a short overview on recent results on simple characters, and I want to introduce a category that is rather elementary to define and still encodes the whole character problem.
This category is the result of joint work with Martina Lanini.[-]