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Here are some specs and comparison of the K03 and the K04.
The exhaust housing is likely going to be different so you will need to take the housing off your K03 and placing it on your K04.
The K04 will bolt right on but really with out the proper software will doing nothing for you.
Stage 3 is not a possible thing for your car with this turbo. And before you do any stage increases on your car be smart and DO YOUR RESEARCH. I can't say exactly what you have done to your car but I can guess that you have nothing done to the internals of this engine.
If anything you might be able to go stage 2 but you will likely need some bolt ons (High flow Cat, High flow exhaust, upgraded divertar valve, upgraded intercooler, upgraded intercooler pipes, etc)

All I can say is RESEARCH RESEARCH RESEARCH before you do anything that could wreck the engine of the car.

Good luck
Rob

VWVortex.com - OFFICIAL: K04-001 Information Thread (click here before making another k04 thread))

5303-988-0053 (AKA K03s)
Compressor part no. 5304 123 2029 (this wheel used in all* 2001+ 1.8t transversal and B6 longitudal)
Compressor size code/Geometry K04-2075E
Inducer: 38.1 (75% of exducer)
Exducer: 51
Tip height: 4.4
Blades: 4 long/4 short
Turbine part no. 5303-120-5037 (used in virtually all 2001+ K03)
Exducer: 40.34
Inducer: 45
Tip height: 6.8
Blades: 11 long

5304-950-0001 (AKA K04-001)
Compressor part no. 5304 123 2010 (this wheel also used in K04-15 upgrade for longitudal)
Compressor size code/Geometry K04-2075E
Inducer: 38.1 (75% of exducer)
Exducer: 51
Tip height: 4.4 (This information is not published; I'm making an educated guess based on the "E' geometry shared with -2029)
Blades: 4 long/4 short (typical of E Geometry wheels)

Turbine part no. 5304 120 5023 (used in K04-15 as well)
Exducer: 42
Inducer: 46
Tip height: 7.6
Blades: 11 long

*excepting Audi 225TT