  The finite entropy of de Sitter space suggests that in a theory of quantum
gravity there are only finitely many states. It has been argued that in this
case there is no action of the de Sitter group consistent with unitarity. In
this note we propose a way out of this if we give up the requirement of having
a hermitian Hamiltonian. We argue that some of the generators of the de Sitter
group act in a novel way, namely by mixing in- and out-states. In this way it
is possible to have a unitary S-matrix that is finite-dimensional and,
moreover, de Sitter-invariant. Using Dirac spinors, we construct a simple toy
model that exhibits these features.
