A flare on 2003 October 28 produced a relativistic particle event at Earth, although the active region AR 10486 was located to the east of the central meridian of the Sun. The paper considers features related to the acceleration at the Sun and the propagation to the Earth of energetic particles in this event, which occurred on a disturbed interplanetary background caused by preceding activity on the Sun and a corotating high-speed solar wind stream. From a study of the onset times of the event at different neutron monitors, we conclude that the earliest arriving solar particles were neutrons. The first relativistic protons arrived a few minutes later. Among relativistic solar protons (RSP), two populations could clearly be distinguished: prompt and delayed ones. The prompt solar protons caused an impulse-like increase at a few neutron monitor stations. The delayed solar protons arrived at Earth 0.5 hours later. Both prompt and delayed relativistic protons arrived at Earth from the antisunward direction. On the other hand, subrelativistic electrons that were traced by their radio emission from meter waves (Nan¿ay Radioheliograph and Decametric Array) to kilometer waves (Wind/WAVES) are accompanied by metric radio emission in the western solar hemisphere, far from the flaring active region. We propose a scenario that reconciles the unusual features of energetic particles at the Earth with the observed structure of the interplanetary magnetic field, which suggests the Earth is at the interface between an interplanetary coronal mass ejection (ICME) and a corotating stream during the event. In this scenario the high-energy protons and electrons are accelerated in the flaring active region, injected into the eastern leg of an ICME loop rooted in the active region, and reach the Earth from the antisunward direction after passing through the summit of the loop. We attribute the promptly escaping subrelativistic electrons to acceleration in the western solar hemisphere and propagation along the nominal Parker spiral.