Tachie had rudely knocked down his opponent Fabian Greilinger in the 88th minute in the game against 1860 Munich and saw the red card from referee Nico Fuchs.
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The DFB now rated the scene as a raw game and banned the 22-year-old for three games. BVB has accepted the ruling, making it legally binding.
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A weakening for the newcomer, the striker has so far been in the starting line-up in all 19 games and has been directly involved in nine goals.