  Under a mild condition, we prove that the action of the group of
self-quasi-isogenies on the set of irreducible components of a Rapoport-Zink
space has finite orbits. Our method allows both ramified and non-basic cases.
As a consequence, we obtain some finiteness results on the representation
obtained from the l-adic cohomology of a Rapoport-Zink tower.
