Liverpool's managing director says Luis Suarez's racist abuse and biting incidents have damaged the club's brand.
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Ian Ayre, though, says the troubled striker "has responded well to ... work on his character."
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Suarez returned on Wednesday against Manchester United from a 10-game ban for biting Chelsea defender Branislav Ivanovic during an English Premier League game in April.
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The Uruguay international had previously been banned for eight games for racially abusing United's Patrice Evra in 2011.
Luis Suarez did not come to the party at all in their game against Manchester United. He was so poor on the night.