What's the URL to your site and more specifically the page with K2 Tools (Archive) module on?

I think you're missing <jdoc:include type="component" /> from your template's index.php file, that's why it appears as though nothing happens. If you do have it, then there must be a check that detects if the current menu item is the homepage and if so, it disables loading <jdoc:include type="component" />. In that case, when you click a link in the K2 Tools module, because these links don't have a menu item assigned to them, Joomla simply re-uses the homepage menu item ID. In which cases it's like you're reloading your frontpage. To bypass that, simply create a menu item in a hidden Joomla menu (=a menu that does not necessarily show up in the frontend of your site) that points to all K2 categories and use a generic menu item alias like "content". This way, provided you're not missing the <jdoc:include type="component" /> tag in your template's index.php file, K2 content will be loaded just fine.