  The homology of the free and the based loop space of a compact globally
symmetric space can be studied through explicit cycles. We use cycles
constructed by Bott and Samelson and by Ziller to study the string topology
coproduct and the Chas-Sullivan product on compact symmetric spaces. We show
that the Chas-Sullivan product for compact symmetric spaces is highly
non-trivial for any rank and we prove that there are many non-nilpotent classes
whose powers correspond to the iteration of closed geodesics. Moreover, we show
that the based string topology coproduct is trivial for compact symmetric
spaces of higher rank and we study the implications of this result for the
string topology coproduct on the free loop space.
