In the fall of 2007, Blackstone Group (BX) had bought Hilton in a $26 billion leveraged buyout at the height of the real estate bubble. Jonathan Gray, Blackstone’s global head of real estate and the architect of the Hilton deal, invested $5.6 billion of Blackstone’s money and had big plans for revitalizing the chain, the epitome of cosmopolitan glamour in the Mad Men era.