UK

Yes, several universities from India have established branch campuses or collaborations with universities in the UK and Australia. These branch campuses offer various degree programs, including Ph.D. programs, to students. Here are a few examples:
Indian School of Business (ISB):
The ISB has a campus in Hyderabad, India, but it also offers a Global Ph.D. programme in collaboration with international partner universities, including the University of Cambridge and the Wharton School of the University of Pennsylvania. While this programme is not specifically in business or procurement, it is worth considering if you are interested in pursuing a Ph.D. in business from an Indian institution with international collaborations. Amity University:
Amity University, which is based in India, has established campuses in the UK and Dubai. They offer a wide range of programs, including Ph.D. programs in business and management. You can explore the options available at their UK campus for a Ph.D. in business with a focus on procurement. Symbiosis International (Deemed University):
Symbiosis International, which is a well-known institution in India, has established a presence in Dubai. They offer a Ph.D. programme in Business Administration at their Dubai campus, which may include specializations in areas such as procurement.