
I saw this image and thought it could work with minor redesign.
Instead of the spring in the back use air pressure to move the bolt. Put the spring in the front to recoil the bolt. The bolt itself will need to be a hollow (like a thick walled pipe) so it can slide over the protruding breech. The breech will need holes drilled in the sides to let in the propelling gases. The rear of the bolt will have a plate that covers the hole so air would not escape.
When the bolt slams foward the plate stops on the back of the barrel, air passes the plate goes through the bolt, entering the peripheral holes and out the barrel. The spring recoils the bolt which picks up the plate off the barrel and seals it again.
A simple magazine feed with a housing, follower, and spring and viola.
Of course a massive chamber at maximum pressure would be required. Using a progressive rate spring I think it could work for burst fire until the spring and the air pressure find their equilibrium. Does this seem feasible? Have I missed something major?