  We consider how the reduced dynamics of an open quantum system coupled to an
environment admits the Poincar\'e symmetry. The reduced dynamics is described
by a dynamical map, which is given by tracing out the environment from the
total unitary evolution without initial correlations. We investigate the
dynamical map which is invariant under the Poincar\'e group. Based on the
unitary representation theory of the Poincar\'e group, we develop a systematic
way to give such a dynamical map. Using this way, we derive the dynamical map
of a massive particle with a finite spin and a massless particle with a finite
spin and a nonzero momentum. The dynamical map of a spinless massive particle
is exemplified and the conservation of the Poincar\'e generators is discussed.
We then find the map with the Poincar\'e invariance and the four-momentum
conservation. Further, we show that the conservation of the angular momentum
and the boost operator makes the map of a spinless massive particle unitary
