you are expecting. Seeing as you haven't really defined the complete
outcome you expect, I will just show you what you need to update the url
with the currently selected store:
$selectBoxOpen = "<select name='store_name'
I've added an onchange event (read more about DOM events here) so that when you select
a different value you are changing the location.
Now when you change the value of the select, your url should change to