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A man was found seriously injured inside a town centre flat.
Officers received a report that the injured man, who is in his 40s, had been found in a room above Domino's pizza in Victory Street, Sheerness, near the junction with Millennium Way, at about 7.45pm on Tuesday.
He received treatment for head injuries from medical crews before being taken to a London hospital.
Police say he remains in a "serious condition".
The man is said to have last been seen in the nearby Hope Street car park at 3pm on Monday.
It is unclear, at this stage, how he suffered the injuries. Detectives are working to establish the full circumstances.
A police forensics van remained outside the former True Briton pub, which is opposite the town's police station, all day on Wednesday. A police car was also parked outside the premises on Thursday.
Investigators are keen to hear from anyone who thinks they can help with inquiries, including those who have video, such as dash cam footage or privately held CCTV, recorded in the area between 3pm on Monday and 7.40pm on Tuesday.
Anyone with information should call police on 01795 419119, quoting the reference 46/228348/21.
Alternatively, to remain anonymous, contact the independent charity Crimestoppers on 0800 555111 or complete the online form on its website.