My 2004 gsxr 600 wont go more then 8000 rpm and the red ligth on speedometer comes on and said check fuel inyeccion

Sounds like clogged or partialy clogged main jets.

Do you have an aftermarket pipe or air filter? It sounds like the bike has a lean spot,and needs to be re-jetted.

THAT WWOULD DEPEND ON HOW MUCH THE DEALER YOU TAKE THE BIKE TO CHARGES PER HOURS LABOUR, FAIRLY EASY JOB

sensor @ trans needs replaced

check corroded wires at connector of the left hand switch coupler

This is hard to tell without riding it to feel the condition. Here are a few things that come to my mind.

1 Spark plugs or ignition system not able to handle the higher demands of the higher RPMs

2 battery or charging system not creating enough power to meet the higher demands of the bike (ignition and fuel systems)

3 Fuel flow to the carbs is low or the main jet is clogged.

4 valve adjustment and or valve timing

its probably your fi light which means fuel injection problem theres a way you can jump the wires which give you a code on the dash like c41 and than that tells you whats wrong heres a link to show you how to do it this is for gsxr 1000 but its the same for your bike.

http://www.gsxr.com/showthread.php?t=63150