Nonhomeomorphic conjugates of connected Shimura varieties

We show that conjugation by an automorphism of ${\Bbb C}$ may change the topological fundamental group of a locally symmetric variety over ${\Bbb C}$. As a consequence, we obtain a large class of algebraic varieties defined over number fields with the property that different embeddings of the number field into ${\Bbb C}$ give complex varieties with nonisomorphic fundamental groups.