What is the object Pope Julius II is holding in his portrait by Raphael? What is the portrait portraying? Why does he look so upset?
I'm not sure about the Pope's right hand, but I can tell you this. He is not considered to be upset, but rather "deep in thought." And the portrait is highly symbolic. Even the acorn's on the back of his chair have meaning.
It looks like a handkerchief, or possibly part of his robe. There is a good article on the painting at Wikipedia, you may search for it.