Can a police officer stop and briefly detain a person for investigative purposes?

"The Fourth Amendment prohibits 'unreasonable searches and seizures' by the Government, and its protections extend to brief investigatory stops of persons or vehicles that fall short of traditional arrest." (U.S. v. Arvizu, supra, 534 U.S. at p. 273.) As a result, "the police can stop and briefly detain a person for investigative purposes if the officer has a reasonable suspicion supported by articulable facts that criminal activity 'may be afoot,' even if the officer lacks probable cause." (U.S. v. Sokolow (1989) 490 U.S. 1, 7.) But "[a]n investigatory stop must be justified by some objective manifestation that the person stopped is, or is about to be, engaged in criminal activity." (United States v. Cortez (1981) 449 U.S. 411, 417.)