Here there is also an issue of overseas direct investment under FEMA as there is no clarity under FEMA regarding investment in LLC.
Depending on the charter documents and specific state rules, one may need to determine if it can be considered as body corporate in India. Whether it is body corporate or not, if it is effectively managed from India, it would be regarded as Indian resident entity and its income would be taxed in India.
For detailed consulation, request you to book telephonic consultation.