A lot! It’s your project. Its success or failure has a lot to do with your leadership. When there is a problem on the project, it is your problem. You may not have to be the one to solve it, but you are the person charged with making sure that it gets solved. You will be held accountable for the successful outcome of the project. Your job includes making your boss and the project sponsor look good. You have wide latitude, but not absolute authority. If you need to assume authority yet doubt that it is yours to claim, ask the project sponsor or your boss for guidance. I suggest you err on the side of assuming too much authority rather than too little.