It should be possible if you can find the CPU - upgrading it will cost you the warranty though - and Dell won't support a CPU upgrade.

But is the motherboard compatible with such a processor? I mean, can I just take one out and insert the other one just like that, with no risk?

Since Dell doesn't offer this CPU in this model, you're on your own to try.  Given the $1,200+ cost of this processor, and the fact that you'll lose your warranty in the process -- it may not be worth trying.

http://www.pcconnection.com/IPA/Shop/Product/Detail.htm?sku=10532131&oext=1038A&ci_src=14110944&ci_sku=10532131

Well I can get it for aroudn €300

http://www.appinformatica.com/procesadores-intel-core-i7-920-2.66ghz-socket-1366-box.php

For me it is worth it since I'm using my pc for chess analisys where cpu power is fundamental.

I just wondered if my mother board was techincally able to host a Core i7 920XM, and if Dell would sell a technician to install it - which I assume is not gonna happen.

Totally agreed - I was mislead by the number 920. And of course I'm not spending that amount in a cpu. Now let's see when is Intel going to release the next generation processor.

That CPU you've linked is a desktop Core i7, not the mobile one.  It cannot be used in any of the Dell mobile systems.  You'd need the 920XM mobile version - which lists for over $1,000 a CPU.  Since it's the top of the line right now, it's highly unlikely you'll find one for much less than that from a reputable seller - it's in short supply. 

The desktop model won't even fit in a notebook socket - the socket 1366 desktop is different from the socket 988 that's used in mobile systems.

Dell will not support any CPU upgrades on mobile systems - you're on your own there.  Given the cost of the CPU right now, I'd wait a while - the price will fall when the next latest and greatest comes along - it always does, and you always pay dearly for Intel's latest and greatest CPU.