Crepant resolutions have inspired connections between birational geometry, derived categories, representation theory, and motivic integration. In this talk, we give a new characterization of log terminal singularities in term of crepant resolutions by stacks. We additionally prove a motivic McKay correspondence, giving the first known description for stringy Hodge numbers in terms of motivically integrating a function that takes only finitely many values. No prior knowledge of stacks will be assumed. This is joint work with Jeremy Usatine.