The intruder managed to escape security guards and stewards, before he was eventually escorted off the field in the Champions League clash at the Parken Stadium.
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The man, who kneeled in the centre circle, was wearing a shirt with the message 'Boycott Qatar' written on it, whilst also holding a miniature football with his hands covered in fake blood.
The game ended in a 1-1 draw, with Thorgan Hazard, the younger brother of Real Madrid star Eden, giving the German side the lead on 23 minutes.
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Danish champions Copenhagen responded, though, when 19-year-old Icelandic midfielder Hakon Arnar Haraldsson equalised on 41 minutes for the hosts.
The World Cup will take place in Qatar later this month, for the first time in the tournament's 92-year history.
It has, however, been the subject of intense scrutiny ever since Qatar won the bid in 2010.
Being openly gay in Qatar is illegal, and the country also has a history of human rights' abuse.
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The treatment of migrant workers has particularly come under the microscope throughout the entirety of the preparation of the competition.
It was reported that thousands of migrant workers who were living in apartment blocks in the capital of Doha were evicted, something Qatari officials deny.
"All have since been rehoused in safe and appropriate accommodation," officials said.
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"Any tenant who believes the terms of their agreement are not being fulfilled may file a complaint with the rental disputes settlements committee office which will review the case and render a decision."