Absolutely. If the police have a warrant for the person's arrest or if they are invited in to the home and see a crime being committed in their presence or if they have exigent circumstances to enter the home and see a crime being committed in their presence they can arrest the person in their home.
A person's home is given special consideration under the law. Generally, a person cannot be arrested in their own home unless the police have a warrant for arrest. A warrantless arrest of a person in their home could lead to the suppression of any evidence seized as a result of that arrest. But as a practical matter, if the police want to arrest you and they know you are in your home, the can stand guard outside and reqeust a warrant be issued by a magistrate, authorizing them to enter and arrest.