DAIOR (Distributed Artificial Intelligence for the OR) aims to develop AI-driven technologies to improve outcomes of patients undergoing surgery, by integrating and analysing massive multimodal data generated in the operating room (OR) in real time through a distributed approach. We envision a future where interconnected ORs continuously receive, send and process knowledge using interoperable artificial intelligence models to promote value-based healthcare. Towards this ambition, this German-French project proposes to prototype and validate the next generation interoperable AI-empowered OR in Europe. DIAOR is centred on two use cases: 1) build and validate a novel surgical environment to leverage OR-based AI Federated Learning (FL) expertise existing in Mannheim & Strasbourg ORs, to ultimately improve patient outcomes; 2) implement an AI solution to enable cross-border robotic telesurgery between interoperable connected operating rooms.