  In the terms of an `$n$-periodic derived category', we describe explicitly
how the orbit category of the bounded derived category of an algebra with
respect to powers of the shift functor embeds in its triangulated hull. We
obtain a large class of algebras whose orbit categories are strictly smaller
than their triangulated hulls and a realization of the phenomenon that an
automorphism need not induce the identity functor on the associated orbit
category.

Representation Theory;Category Theory;Rings and Algebras