Did you sign for any money on the original repair order? If you didn't and they said it's going to be covered under warranty, you shouldn't have to pay a dime to at least get it out of there. If there's a question of whether something is going to be covered or not, a good service writer will get you to sign for some amount of money to pay for the inspection and diagnosis. If it's covered, you don't pay the estimate, if it's not, you pay what you agreed to pay. If they didn't have you sign for any money to check it out, you pay nothing. If they're not smart enough to know if it's covered or not, that's their problem.
If you put the downpipe on yourself, then you can probably put the turbo back on yourself too. Actually, I believe the law reads that if they take it apart to figure out what's wrong with it, and they haven't told you that you have to pay anything before taking it apart, they have to put it back together for free. In other words, if you never agreed to pay for anything, they should return your car in the condition they got it in.
Don't quote me on any of this, I'm a tech not a writer. I believe the laws regarding auto repair are similar across the country so I should be right on this. The key is whether you signed for any money or not. Or if they gave you an updated estimate of repairs or diagnosis time in which you agreed to pay.
Like Dave said, the cracks in the turbo and exhaust manifold are not normal, but very common. (I've never seen one that wasn't cracked.) And he's also correct, if there was an exhaust leak ahead of the Lambda or 02 sensor it would read a false lean condition which would make the motor run too rich, not too lean. Even if it was running lean like they said, it's unlikely that it would "cause the turbo to leak". Leaking what? Tell them to prove what they're talking about or give you your car back.
As far as getting the repair covered under warranty, you really should have known better than that. You put an aftermarket part on, an emission part at that, and brought it in to the dealer expecting them to cover it under warranty. If the dealer wants to be snotty about it, they can call GM and have your powertrain warranty blocked (voided) because of the modified emission control item. If you plan on going to this dealer in the future, you might want to play nice and figure out a solution that's fair for both of you. (Like paying the labor it took them to diagnose the problem, not to take off a turbo that may or may not have a problem.) Or if you really do need a new turbo, tell them you really don't think the downpipe had anything to do with the turbo failure so how about they warranty the part (turbo) and you'll pay all the labor. Or vise-versa, you pay for the turbo and they eat the labor. Not to be too mean, but you blew it by not pulling the cover off the turbo and checking the aftermarket downpipe yourself. Now that you're in this situation, it might end up costing you some cash to get out of it.
