* Transmission limitations: The Cavalier's automatic transmission wasn't designed for the increased torque a turbocharger would produce. It's highly likely to fail prematurely, potentially causing catastrophic damage to the transmission and other drivetrain components. You'd likely need a significant transmission upgrade or rebuild, which is expensive and complex.
* Engine limitations: The Cavalier's engine, depending on the year and model, might not be robust enough to handle the increased stress of forced induction. Internal components like pistons, connecting rods, and the crankshaft could be susceptible to failure. Strengthening these components would require internal engine modifications, increasing the project's complexity and cost.
* Computer control: The factory engine management system (ECU) isn't designed for a turbocharger. You'd need a standalone engine management system or significant tuning of the factory ECU to properly control fuel delivery, ignition timing, and boost pressure to prevent engine damage. This is a technically challenging aspect requiring specialized knowledge.
* Cost: The overall cost of a turbocharger kit, transmission upgrades (or replacement), engine strengthening, and professional tuning could easily exceed the value of the car, especially considering the labor involved.
In short, while technically possible, turbocharging an automatic Chevy Cavalier is a very complex and potentially expensive project with a high risk of failure. Unless you have significant mechanical and tuning expertise, and are prepared for a substantial investment, it's generally not a worthwhile undertaking. The effort and cost would likely be better spent on purchasing a car already equipped with a turbocharger.