Question : can I make a website in a subdirectory appear as the main site in google searches?

I have a website in a subdirectory of my web server. I have a URL forward to the subdirectory, only when I google search for this site the full url including the main sites address is shown.

is there a way to make search engines find the correct url (www.mynewsite.com) instead of the full path (www.existingsite.com/mynewsite/default.htm)?

Answer : can I make a website in a subdirectory appear as the main site in google searches?

I think becuase the url is setup as a 'forward'  it is not an address - can you set it up as an alias instead?
do you use the full path in your links in your website or the 'correct url'?