The talk will be based on joint work with Finkelberg, Ostrik and also with Kazhdan and Varshavsky. Character sheaves (or D-modules) can be described as categorical (Drinfeld) center of the Hecke category (this idea was also independently worked out by Ben-Zvi and Nadler in a different context). This provides a new way to derive their classification and partly generalize the theory to loop groups."