For twelve years he was a member of the art collective Los Carpinteros, until he left the group in July 2003 to continue his career as a solo artist.
Arrechea made his name thanks to the art collective Los Carpinteros, composed of Marco Antonio Castillo Valdés and Dagoberto Rodríguez Sánchez.
His first individual project was El Jardin de la Desconfianza (The Garden of Mistrust), an epic installation in Los Angeles that required two years of work (2003-2005).
The central piece of the work was a whitewashed aluminum tree whose branches were outfitted with video cameras which recorded spectators and broadcast them on the Internet.
For the 10th Havana Biennial (March 27 – April 30, 2009), Arrechea worked on a project named La habitación de todos (The Room of All), which is a sculpture of a house that expands or contracts according to, respectively, the rise or fall of the Dow Jones Industrial Average.