Yes, there are international schools in India catering in different international boards like IGCSE, ICSE, and Ontario etc.
They provide K-12 educational meaning Kindergarten to 12th standard.
But nomenclature of standard/classes is different, example: IGSCE call 1st standard as PP1 and 2nd as PP2 and CP1 for 5th so on. Also the examination pattern will be different.
Approximately there are around 200 international schools that are functioning in India and those are located in all type of metropolitan and cosmopolitan cities like Delhi, Greater Faridabad, Lucknow, Bangalore, Mumbai, Chennai, Namakal etc.
City Montessori school in Lucknow (ICSE syllabus) is world largest school with strength around 50,000 plus students. And all these schools are recognized by government of India.