The classical Nilpotence and Periodicity theorems in stable homotopy theory lead to a satisfying classification of possible nonnilpotent self-maps of finite spectra. In motivic homotopy theory over C, the obvious analogue can't hold. For example, the Hopf map eta is not nilpotent here. By work of Gheorghe, this is part of an infinite family of self-maps, all detected by exotic motivic K-theories. In this talk, I want to discuss a generalization of these results leading to a bigger class of self-maps, exotic K-theories and an associated chromatic filtration on motivic homotopy groups over C.