Step 1: Identify the award.
The G.V. Raja Award is named after G.V. Raja, a distinguished sports administrator and politician from Kerala. It is presented annually by the Government of Kerala to recognise outstanding sporting achievement.
Step 2: Confirm the state.
The Government of Kerala instituted this award as the highest sporting honour in the state, celebrating athletes who have brought pride to Kerala on national and international platforms.
Step 3: Eliminate other options.
Karnataka, Telangana, and Tamil Nadu each have their own state sporting honours, but the G.V. Raja Award belongs exclusively to Kerala.
\[ \boxed{\text{Kerala}} \]