  The minimizers of the anisotropic fractional isoperimetric inequality with
respect to the convex body $K$ in $\mathbb{R}^n$ are shown to be equivalent to
star bodies whenever $K$ is strictly convex and unconditional.
  From this a P\'olya-Szeg\"o principle for anisotropic fractional seminorms is
derived by using symmetrization with respect to star bodies.
