Making a Chrome Extension execute Javascript code in the page execution context

Update: in order to execute a script in any open tab inside Chrome, use the executeScript method of the tabs API.

Chrome browser extensions are so cool, that they protect you from accidentally running and adding script to a page that might interfere with the original code of the page. Unfortunately, they don't give you a parameter or option to actually do that, if it is what you actually want. All you can do, by default, is to access the elements in the page document, but not change direct members of window or even document.

I have found the solution on this page: Writing a Google Chrome extension: How to access the global context of the embedding page through a content script.. There is code and explanations for the code, but basically it is a function that injects another function in the real page context and also returns a result.