Elon Musk’s artificial intelligence company xAI has established an Irish entity. XAI, which is behind the Grok AI chatbot, was set up by the billionaire in 2023 and competes with the likes of OpenAI. Its AI applications have been deeply entwined with social media site X, which he also owns. The Irish company – X.AI Management Company Ireland Limited – was registered on Tuesday this week and lists an address in Cork. The company’s only director so far is Texas-based Jared Birchall, a key lieutenant in Musk’s various businesses. He is the chief financial officer of xAI and chief executive…