Let's say you placed some sort of biological material (like raw chicken meat, an apple, etc.) in a very large glass container (large enough that moisture could evaporate at a similar rate to the normal atmosphere); filled it with a heavier-than-air, inert gas, like xenon; then, sealed the container and placed it outside.
Question: Would the biological material decompose?
My natural assumption is that it would decompose slightly, but mostly it would dry out and essentially become "mummified."
I think your experiment is along the same lines as one performed in 1680 by Antonie van Leeuwenhoek. His experiment is described in this Wikipedia article:
In his letter of 14 June 1680 to The Royal Society, Antonie van Leeuwenhoek described an experiment he carried out by filling two identical glass tubes about halfway with crushed pepper powder, to which some clean rain water was added. Van Leeuwenhoek sealed one of the glass tubes by using a flame and left the other glass tube open. Several days later, he discovered in the open glass tube ‘a great many very little animalcules, of divers sort having its own particular motion.’ Not expecting to see any life in the sealed glass tube, Van Leeuwenhoek saw to his surprise ‘a kind of living animalcules that were round and bigger than the biggest sort that I have said were in the other water.’ The conditions in the sealed tube had become quite anaerobic owing to consumption of oxygen by aerobic microorganisms.
Obviously his experiment was not as tightly controlled as what you propose. Also, I think the actual size of your "very large glass container" would be the key to microbial activity in your experiment, as anaerobes do require water to thrive. It sounds like van Leeuwenhoek gave his bugs plenty water for the scale of his experiment.
My guess is that there would be some anaerobic decomposition before it pretty much dried out and "mummified".
