Redirect subdomain to subfolder of another subdomain

What I want to do is take traffic that is going to shop.mywebsite.com and redirec开发者_StackOverflowt or rewrite (I'm not sure of the terminology) the domain to be www.mywebsite.com/shop. Both shop.* and www.* are separate web applications (nopCommerce and Umbraco respectively) that don't seem to cooperate when I've tried to nest them. Both applications are in a Server 2008 R2/IIS 7.5 environment.

I've searched around stackoverflow and what I've found is a lot of answers to mapping the other direction (ie subfolder to a subdomain) but that's not what I'm looking for as far as I understand the problem.

The end goal is to combine the SEO reputation of the shop subdomain into the www subdomain. I readily admit that I might have this all backwards and am willing to try any suggestions I'm offered.

Thanks.

I think you are looking for URL rewriting.

URL rewriting is the process of intercepting an incoming Web request and redirecting the request to a different resource. When performing URL rewriting, typically the URL being requested is checked and, based on its value, the request is redirected to a different URL

EDIT: You may also want to check URL Rewrite Extension from microsoft, it will fix common SEO problems that your site might have.