The amount of horsepower that a turbocharged car can produce is reduced at altitude but since the induction air is compressed entering the intake, a turbocharged car suffers less degradation of performance with increasing altitude than a normally aspirated car. The engine management software can allow the wastegate to increase the boost pressure to maintain sea level horsepower up to a point but, at a high enough altitude, the amount of oxygen in the air is so limited that system cannot continue to compensate with more turbo boost because of the potential for engine damage from detonation. And yes, there is less oxygen per given volume of air at higher altitudes. The proportions of different gases that make up air remain the same but they take up more volume. A good illustration is to realize that physical activity in, say, Boulder, CO is more difficult because less oxygen is available in the air. But if we could force more air into our lungs at this altitude, we could get the same number of Oxygen molecules and not get fatigued walking up a flight of stairs. That is the job of a turbocharger....to force more air into the engine than it could get without a turbo.

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