Yes. Police have the power to arrest people suspected of having committed a crime. It is prosecution's job to prove that you shoplifted. You might want to hire a criminal attorney in your area. This is a serious matter and you could end up with a criminal record.
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Actually, if the charge is a simple misdemeanor, the police cannot arrest you in these circumstances without a warrant. A misdemeanor goes "stale" and the police must seek a warrant for your arrest on a misdemeanor unless it is a current, ongoing investigation. Even then, if it was a misdemeanor, the police couldn't arrest you for the charges, since I assume the crime wasn't committed in their presence. It would require a private person's arrest.
If they suspect that you entered with the intent to steal, that's burglary and is a potential felony, allowing them to arrest without a warrant based on probable cause.
Enough of the criminal procedure, though. Either way, you're facing criminal charges, so it's time to consult with a criminal defense attorney to discuss the particulars of your case in detail.