When a drop-down list is created from a ul tag, it appears to not be treated as a control that can be tabbed to. The following definitely occurs with Chrome. I have not been tested this with other browsers.
Control created with ‘source’ field: Go to the page at http://www.jqwidgets.com/jquery-widgets-demo/demos/jqxdropdownlist/defaultfunctionality.htm?arctic, click in the address bar, hit tab twice, then pressing an arrow key will cycle through the drop down options, demonstrating the control has focus. On the third press of the tab key, the focus will again be in the browser’s address bar.
Control create with ‘ul’ tag: Go the page at http://www.jqwidgets.com/jquery-widgets-demo/demos/jqxdropdownlist/dropdownlist-from-ul.htm?arctic, repeat the above test. When the control should have focus, it does not get highlighted indicating it has focus, not does it respond to the arrow keys. Hitting the tab key for a third time, focus is returned to the browser’s address bar.
–jcwren