Representation theory of groups, rings and algebras describes and compares categories of modules or representations, or related categories such as derived or stable categories. Equivalences between such categories need to be studied in order to reduce new examples to known ones and to exhibit new connections between seemingly different situations. While the classical notion of Morita equivalence is well known, much less is known about equivalences of derived or stable categories, which are the source of major current problems and conjectures. This project will study stable equivalences of Morita type, which form the class of stable equivalences needed in most applications and which are closest to derived equivalences. A general theory needs to be built, connections and comparisons with derived equivalences have to be clarified or established, and applications, e.g. in representation theory of finite groups and in algebraic Lie theory, are envisaged. The project will support an outstanding young Chinese researcher in becoming a research leader in his home country.