Chrome Extension - add Div over page view

Is there a way in chrome extensions to add a div OVER the page view, not to the page. I want that when I switch to 开发者_开发技巧another tab, the div is still there. The div should not be a part of the page, but over every page.

When this is possible: How?

No such thing.

You would need to add a div to each tab and then sync its content by exchanging messages with a background page (or make it iframe linked to extension's html page).