Non-Archimedean integrals and stringy Euler numbers of log-terminal pairs

Using non-Archimedian integration over spaces of arcs of algebraic varieties,we define stringy Euler numbers associated with arbitrary Kawamata log terminalpairs. There is a natural Kawamata log terminal pair corresponding to analgebraic variety V having a regular action of a finite group G. In thissituation we show that the stringy Euler number of this pair coincides with thephysicists' orbifold Euler number defined by the Dixon-Harvey-Vafa-Wittenformula. As an application, we prove a conjecture of Miles Reid on the Eulernumbers of crepant desingularizations of Gorenstein quotient singularities.