I'm afraid you're on your own, Per. When I got my AT-44, it was very stiff and gritty, and the trigger was terrible. Tearing it down was a challenge, this is the only exploded diagram I could find: http://www.umarexusa.com/umarex/images/partsdrawings2/Pneuma.jpg
Not very helpful. Still, it's not that difficult, just take your time and don't force anything. Once I had it apart, I cleaned everything thoroughly, polished the hammer tube, hammer/striker, and bolt, then lubed sparingly with some moly. That had the rifle functioning smoothly, but the trigger was still terrible. So I pulled it again and studied the way it works. Despite the claims, it's a single stage trigger, the "first" stage is nothing but a spring. Then there are two heavy springs on the trigger sear. Finally, the design of the safety adds some drag to the whole system. Since a pic is worth a bunch of words, here it is:
The spring and associated parts at the rear of the trigger all got removed, as well as the useless pull weight adjusting screw. With the "first stage" adjusted as short as I could get it, it brought the trigger blade too far back for my comfort. So I cut a small nail to fit, and slipped it inside the spring in the trigger blade, and used the adjustment screw to lock it down. All this resulted in a crisp, light single stage trigger that I could now use without constantly pulling myself off target. Oh, and I eliminated the safety. As I said, it was adding increased drag to the trigger system, and I hate automatic safeties, anyway.
After this was all done, my .177 rifle was getting almost 25 fpe with CPH's, and was very accurate, although somewhat inconsistent. That seems to be an issue with either the synthetic stock or the barrel bands, the problem cleared up for me when I traded the synthetic stock for a wood one.
The last problem was a leak in the air cylinder at the valve. This one is still unresolved, I've tried several fixes that all worked for awhile, but then it would start leaking again. Not sure what the problem is, but I suspect it's the Delrin valve seat, which is available from Umarex here, not sure where you'd get parts there.
All told, I probably have 3-4 hours of tinkering in this rifle, the result being a smooth, accurate rifle that has good power, and would make an excellent hunter. I hope this is some help, and if you have any specific questions, feel free to email me directly. Later.