to create a new tab use chrome.tabs.create(Object properties, function callback) as described on http://code.google.com/chrome/extensions/tabs.html
The object properties could contain fields for windowId, index, url and selected. The optional callback function receives a Tab object of the newly created tab.
Not sure why you would like to show the popup.html in a new tab, but I find it very useful while developing/debugging my extension ... it is quite a pain that on the extension page there is "usually" only a link to the background page.
So the simplest example to create a new tab in the current window and get it selected would look like this:
chrome.tabs.create({'url': chrome.extension.getURL('popup.html'), 'selected': 'true'});
Would love to know how to open it in a new window and maybe in a kiosk mode ;-)