The Colombian was followed by police to Madrid's Valdebebas training ground in the north of the city on January 1 after being caught speeding by an unmarked police car.
"He has been sanctioned for not obeying the agents that tried to detain him on various occasions," Concepecion Dancausa said in a press conference.
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On top of the fine, the 24-year-old faces a separate judicial process for speeding.
The fine is the maximum amount that can be imposed for a serious case of disobedience or resistance towards the authorities.
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According to press reports, the top scorer at the 2014 World Cup defended his actions once he stopped for the officers inside the training ground by claiming he feared he was being pursued by kidnappers.
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