is it possible to swap a 2.2 to a 2.0 supercharged in a 2004 cavie can that be done with out a hole lot of work
Nope, search around, there are a few reasons why, I can't recall any off the top of my head because I've never really looked into it, but I'm sure somebody will chime in.
the one big thing I think was the drive by wire on the TB.
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Nowhere as hard as many people make it to be. It is prohibitively expensive if your buying an LSJ crate though.
To do the swapp all you need to do is bolt up the assembly and get an adapter for the L61 throttle body(just like in the SC kit) and then fit and plumb up an aftercooler heat exchanger assembly. If youve got the money or access to a cheap LSJ go for it. Its a better option than the supercharger kit because you get the better supercharger, the bitchin sandcast head, and all of the other niceties thatgo along with the LSJ.
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Something about the transmission being too large to physically fit in a J-body... I guess that might be a problem?
if you where going to do it you pretty much need to buy a complete wrecked cobalt SS S/C to make it work. i have seen a few around. the last cobalt SS S/C we got at work was slammed from behind the rear bumper was pushed up almost against the front seats and they paid $5400 for it. but if you take a whole car you will get 95% of the parts you will need for the swap.
one thing i noticed is the strange engine cross member on the cobalts, you might have to custom make a cross member for it to work.
as for the tranny being to big im not sure, but there not much bigger then a cavalier tranny so theres a pretty good chance that you could make it fit.
hope this helps.
http://registry.gmenthusiast.com/images/my2005cav/my%20car%20the%20bash.jpg