Ah... this is due to the base URL, and it just happens to manifest itself in the AjaxSearch, but it also comes up with auto-generated links to any pages that are deeper than the root of the site. This problem comes up with multiple CMS applications and with multiple browsers -- I’ve seen IE and FF also choke over various URL configurations, but I’m still not sure what exactly causes it... I just know how to avoid it.
The solution is to add a base tag to the head of your templates:
<base href="http://www.yourdomain.com/"/>
Often I combine this with a Snippet so I can copy the site to my dev server without having to edit the templates after the move, i.e.
In my templates:
<base href="[[site_url]]"/>
Contents of site_url Snippet:
<?php
echo 'http://' . $_SERVER['SERVER_NAME'];
?>
Hope this helps.