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A man has been arrested on suspicion of murder after an attack near a parade of shops in Ashford.
The victim - who was in his 40s and from the town - died in hospital on Saturday after suffering a serious head injury.
Police taped off a grassy area next to the Co-op off Brookfield Road at about 8.30pm on Thursday, December 21.
On Sunday, officers arrested a 30-year-old man from the Ashford area in Bexleyheath on suspicion of murder.
He has been bailed until Friday, January 26.
A police spokesman said a post mortem is being carried out this week to determine the cause of death.
Inquiries to establish the circumstances of his death are ongoing.
At the time of the incident, the police tape surrounded a patch of grass measuring about 50 yards by 40 yards behind the shops and in front of homes on a neighbouring housing estate.
Inside the cordon there were three small yellow markers with the numbers one, two and three on them.
Anyone with information about the incident is asked to phone police on 01843 222289, quoting reference number ZY/063177/17.