It is possible with "URL Rewriting" or "Friendly Urls" (name varries depending on who you talk to / read)
It is a diffuclt topic to explain easily in a post like this - although essentially the technique is quite simple - so I'd suggest you try and Google url rewrite http module.

But basically - what often is done is you develop a "http module" (basically a class library) which you attach to the website. That module will be hit on incoming requests and read the (external) url and map it and rewrite it to a another (internal) url.
So your users will see one url, but the system internally will see another.