If you are looking for international brands, H&M or exclusive international boutiques such as Gucci and Chanel, you should go to the downtown area of Copenhagen. On Strøget, the main pedestrian street, the large, internationally famous brands can be found.
On the longest pedestrian street in Europe, Strøget, you will find most international brands. Strøget is the popular name for a number of streets leading from the City Hall Square to Kongens Nytorv. Near the City Hall Square are the young, international chain stores such as H&M and Zara. H&M is also in Købmagergade as is Diesel and Benetton.
If you go further up towards Kongens Nytorv you will see the more exclusive brands. Here are Gucci, Max Mara, Louis Vuitton, Mulberry, Chanel, Birger Christensen Furs, Marlboro, Marc Jacobs, Karen Miller, Ralph Lauren and Hermès.
Birger Christensen 
The only place in Copenhagen, where you can purchase Chanel products. Also Prada, Armani, Hermès, Yamamoto, D&G, DKNY, Marc Jacobs, Miu Miu and Yves Saint Laurent for men and women.
Østergade 38
1100 København K
Tel: +45 33 11 55 55
Gucci 
Østergade 46
1100 København K
Tel: +45 33 36 68 83
Karen Millen 
Købmagergade 28
1100 København
Tel: +45 33 33 06 88
Louis Vuitton 
Østergade 18
1100 København K
Tel: +45 33 15 10 22
Marc by Marc Jacobs
Christian IX's Gade 3-5
1111 København K.
Read more here
Marlboro Classics 
Østergade 15
1100 København K
Tel: +45 33 13 10 33
Max Mara Shop 
Østergade 7-9
1100 København K
Tel: +45 33 38 56 20
Mulberry 
Østergade 13
1100 København K
Tel: +45 33 36 68 78
In Illum, you can purchase the international brands mentioned below:
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Burberry
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Hugo Boss
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Kenzo
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Marlboro Classics
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Ralph Lauren Illum
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Tommy Hilfiger
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Van Gils