Final answer:
The 1913 play by George Bernard Shaw that is based on an ancient Greek myth recounted by Ovid is Pygmalion.
Step-by-step explanation:
The 1913 George Bernard Shaw play that was based on an ancient Greek myth recounted by Ovid is Pygmalion. In this play, Shaw explores the superficiality of society by telling the story of a flower girl who is transformed into a lady of society by changing her pattern of speech. Pygmalion later became the basis for the popular musical, My Fair Lady.