European Bee-Eater (Merops apiaster) has a very similar breeding range to European Roller.
It breeds in all but the most northern parts of a region stretching from Western Europe to Central Asia. Almost the entire global population winters in southern and central Africa but a small number spend the winter in Sri Lanka and along (and adjacent to) the Kaveri river in southern Karnataka and northern Tamil Nadu in India.
This incredibly beautiful bird is one of the most conspicuous migrants in Europe. During passage in autumn and spring, you can hear them calling distinctively while migrating high up in the sky.
In India, European Bee-Eater breeds in parts of Kashmir but it is unclear whether those birds winter in South India or go to Africa. Perhaps the story will unravel soon as more birdwatchers record them during passage in India.