Explore the relationship between tracial states and G-invariant states on quantum group reduced C*-algebras in this 34-minute lecture by Benjamin Anderson-Sackaney from Université de Caen-Normandie. Delve into the analogy between conjugation-invariant states on discrete group C*-algebras and their quantum counterparts. Examine recent findings by Kalantar, Kasprzak, Skalski, and Vergnioux revealing a correspondence between G-invariant states and KMS-states, highlighting differences between tracial and G-invariant states for non-unimodular quantum groups. Discover how the connection between traceability and G-invariance can still provide valuable insights into the tracial states of C_r(ℏG), despite these disparities.