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We establish explicit quenched asymptotics for pure-jump symmetric L\'evyprocesses in general Poissonian potentials, which is closely related to largetime asymptotic behavior of solutions to the nonlocal parabolic Andersonproblem with Poissonian interaction. In particular, when the density functionwith respect to the Lebesgue measure of the associated L\'evy measure is givenby $$\rho(z)= \frac{1}{|z|^{d+\alpha}}\I_{\{|z|\le 1\}}+e^{-c|z|^\theta}\I_{\{|z|> 1\}}$$ for some $\alpha\in (0,2)$, $\theta\in(0,\infty]$ and $c>0$, exact quenched asymptotics is derived for potentialswith the shape function given by $\varphi(x)=1\wedge |x|^{-d-\beta}$ for$\beta\in (0,\infty]$ with $\beta\neq 2$. We also discuss quenched asymptoticsin the critical case (e.g.,\, $\beta=2$ in the example mentioned above).

Quenched asymptotics for symmetric L\'evy processes interacting with Poissonian fields