abstract: In this talk, I will present a joint project with Peter Fiebig, aimed at developing new tools to attack problems in the representation theory of complex affine Kac-Moody algebras and algebraic groups in positive characteristic. I will introduce a new combinatorial category, realised using moment graph techniques, which exhibits a certain periodicity behaviour. The periodic patterns appearing in our category are the same expected to govern certain multiplicity formulae for representations of the above mentioned objects.