L.A.: 'Tempest' of genius; skillful 'Brain Hotel'

The depth of the international theatrical riches offered by the Los Angeles Olympic Arts Festival is unprecedented on these shores. London's Royal Shakespeare Company, Paris's Theatre du Soleil, Milan's Piccolo Teatro, Montreal's Theatre Sans Fil, the China Performing Arts Company, and Boston's American Repertory Theatre, are among the 19 troupes invited to take part. Eleven Los Angeles-based troupes were given a chance to show off their unique gifts, too.

During a week here I've had a chance to see the Piccolo Teatro di Milano - under the direction of founder Giorgio Strehler - present Shakespeare's ''The Tempest'' (which has now moved on to PepsiCo Summerfare '84 in Purchase, N.Y.). Previous tours of this company have afforded us precious few glimpses of Strehler's theatrical genius.

In this ''Tempest,'' every last detail is thought through. Every gesture has crucial meaning. The stage is at once universe, tableau, and reality. Strehler presents the play as a study in the manipulation of theatrical artifices - the appearance of reality vs. reality itself.

On Luciano Damiani's brilliant set, it is the last day of Prospero's artificial reign over his island. Lighting accentuates the day's progress, and Strehler is particularly alert to shades and shadows amplifying a mood. A billowing piece of fabric, some flashing strobe lights, and a suspended actress flapping gossamer wings make up a vision of terrifying strength; the storm that opens the play is a miracle of impressionistic verisimilitude - from the crashing waves and the rocking frigate to the vision of the mast splitting in two as the vessel founders.

But in all this magic, this illusion, there is great humanity, as well as suffering, strife and chicanery, love and hate. Strehler's Prospero knows how tenuous his world is, how mighty the struggle to keep it all going, and how easily the results of his magic can become hollow, even cruel. When Prospero finally breaks his rod, we are left with the devastating vision of a setless stage in shambles which ''miraculously'' becomes its theatrical self at the final curtain. Strehler's view of Caliban the slave is not villainous, but nobly savage, untrained in guile and subtlety - a figure of tragedy.

Strehler often brings the action in front of the proscenium arch: Prospero stands outside his world looking in; liberated, Ariel runs skittishly into the audience and out the back doors.

The acting was uniformly fine (although the cavernous acoustics of Royce Auditorium made grasping the Italian particularly chancy). One sensed throughout an ensemble dedicated to excellence. Nevertheless, Giulia Lazzarini's Ariel proved particularly affecting, as did Fabiana Udenio's simple but heartfelt Miranda and Michele Placido's noble Caliban. Cast Theater

On a different level, the Hollywood-based Cast Theatre offered an intriguing, intimate, original musical, ''Brain Hotel''. Four performers - calling themselves Body, Heart, Mind, Soul - ''check'' into a hotel where odd fantastical events involve them all, as expressed by their particular profile.

Everything is sung, including the stylized dialogue. Musically it veers from pop to Rodgers to Bernstein, by way of Sondheim and Weill. What could have reeked with pretension becomes instead an engaging, amusing, often insightful hour and a half of musical adventure, produced by Ted Schmitt on a shoestring and directed by Tony Abatemarco with skill, love, and imagination.