  This note treats several problems for the fractional perimeter or
$s$-perimeter on the sphere. The spherical fractional isoperimetric inequality
is established. It turns out that the equality cases are exactly the spherical
caps. Furthermore, the convergence of fractional perimeters to the surface area
as $s \nearrow 1$ is proven. It is shown that their limit as $s \searrow
-\infty$ can be expressed in terms of the volume.
