Joomla cookies are assigned to root path even if site is in a subfolder.

This means that if you have several Joomla installations under one domain, they will all use the same cookies and, for example, "think" that your joomla_user_state is "logged_in" in all sites even if it may be just logged in one site.

This can create all kind of conflicts and unexpected behaviors.

Steps to reproduce the issue

1. Create a Joomla site in a subdirectory such as www.mysite.com/joomlainstall/
2. After logging in, check the stored cookies (joomla_user_state, session cookie, joomla_remember_me...)

Expected result

They should be assigned to the proper root path of the specific installation "/joomlainstall/"

This allows you to have separate cookies for each separate installation under the same domain.

Actual result

They are currently assigned to the root path of the whole domain "/"