What do the decomposers do to return atoms back to the biogeochemical cycles?

they take organic matter and render it in inorganic form

Explanation:

both anaerobic and aerobic respiration use glucose (or other carbohydrates), proteins and lipids to produce atp and nadh. cell uses those energy molecules, obtained from food and   breaks them down during the chemical reactions of respiration. in anaerobic respiration, nadh is regenerated to nad+ by enzymes lactate dehydrogenase (lactate is produced, e.g. in muscle cells) or by alcohol dehydrogenase where ethanol is produced (alcohol fermentation), while in aerobic respiration, electrons from nadh are deposited in the mitochondria to regenerate nad+ (electron transport chain. anaerobic respiration produces 2 atp per molecule of glucose compared to aerobic respiration where about 38 atp molecules are produced.