When you set up URL forwarding, you may use web address mapping to forward subdomains, such as www.your_domain.com or home.your_domain.com, to particular Google Sites.
To do this, follow the instructions for Mapping your site to your own URL. Then follow the instructions provided to create a CNAME record of "www" pointing to "ghs.googlehosted.com" with your domain host.
If the site is public, users who are not signed in to the site will remain on www.your_site.com while navigating the Site. (If there is a Sign in link on the bottom of the page, you are not signed in to the site.) Users who are signed into the site, regardless of whether it is private or public, will see the original sites.google.com/a/your_domain.com/your_site address.