  Let E be a finite dimensional vector space over an algebraic closure of a
finite field with a given linear action of a connected linear algebraic group K
and let E' be the dual space. A complex of l-adic sheaves on E is said to be
orbital if it is a simple perverse sheaf whose support is a single K-orbit. A
complex of l-adic sheaves on E is said to be biorbital if it is orbital and if
its Deligne Fourier transform is orbital on E'. In this paper we study examples
of biorbital complexes arising in the case where E is an eigenspace of a
semisimple automorphism of a reductive Lie algebra.
