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We establish the quenched large time asymptotics for the Feynman-Kac functional [formula] associated with a pure-jump symmetric Lévy process (Zt)t⩾0 in general Poissonian random potentials V ω on Rd, which is closely related to the large time asymptotic behavior of solutions to the nonlocal parabolic Anderson problem with Poissonian interaction. In particular, when the density function with respect...