General synonyms:
* Return
* Reversion
* Restoration
* Bringing back
* Sending back
* Returning home
More specific synonyms:
* Repatriation of funds: Remittance
* Repatriation of refugees: Resettlement
* Repatriation of cultural artifacts: Return of cultural property
The best synonym will depend on the specific situation. For example, if you're talking about the return of refugees to their home country, "resettlement" might be the most appropriate term.