Question: Which character did Richard Burbage play that is derived from the legend of Leir of Britain?

Context articles: Nicholas Brend
Shakespeare in performance
Cuthbert Burbage
Richard Burbage
Richard Sharpe (actor)
Leir of Britain
Richard Cowley
King Lear
King Leir
Matthew Brend

Nicholas Brend (c. 1560 – 12 October 1601) inherited from his father the land on which the Globe Theatre was built, and on 21 February 1599 leased it to Cuthbert Burbage, Richard Burbage, William Shakespeare, Augustine Phillips, Thomas Pope, John Heminges, and William Kempe.
 He died two years later, leaving the property on which the Globe was built to his infant son, Matthew Brend, who did not come of age until 6 February 1621.
Thousands (perhaps even millions) of performances of William Shakespeare's plays have been staged since the end of the 16th century.
 While Shakespeare was alive, many of his greatest plays were performed by the Lord Chamberlain's Men and King's Men acting companies at the Globe and Blackfriars Theatres. Among the actors of these original performances were Richard Burbage (who played the title role in the first performances of "Hamlet", "Othello", "Richard III" and "King Lear"), Richard Cowley, and William Kempe.
Cuthbert Burbage (c. 15 June 1565 – 15 September 1636) was an English theatrical figure, son of James Burbage, builder of the Theatre in Shoreditch and elder brother of the actor Richard Burbage.
 From 1589 he was the owner of the ground lease of the Theatre.
 Best known for his central role in the construction of the Globe Theatre, he was for four decades a significant agent in the success and endurance of Shakespeare's company, the King's Men.
Richard Burbage (6 January 1567 – 12 March 1619) is considered the first great actor of English theatre.
 He is one of the most famous actors of the Globe Theatre of his time.
 In addition to being a stage actor he was also a theatre owner, entrepreneur and painter.
 He was the younger brother of Cuthbert Burbage.
 They were both actors in drama.
 Burbage was a business associate and friend to William Shakespeare.
Richard Sharpe (c. 1602 [?]
 – January 1632) was an actor with the King's Men, the leading theatre troupe of its time and the company of William Shakespeare and Richard Burbage.
 Sharpe began his career as a boy player acting female roles, then switched to male roles in his young adulthood.
Leir was a legendary king of the Britons whose story was recounted by Geoffrey of Monmouth in his pseudohistorical 12th-century "History of the Kings of Britain".
 According to Geoffrey's genealogy of the British dynasty, Leir's reign would have occurred around the 8th century BC, around the time of the founding of Rome.
 The story was modified and retold by William Shakespeare in his Jacobean tragedy "King Lear".
Richard Cowley (died 1619) was an actor in English Renaissance theatre, a colleague of William Shakespeare and Richard Burbage in the Lord Chamberlain's Men and the King's Men.
King Lear is a tragedy written by William Shakespeare.
 It depicts the gradual descent into madness of the title character, after he disposes of his kingdom giving bequests to two of his three daughters based on their flattery of him, bringing tragic consequences for all.
 Derived from the legend of Leir of Britain, a mythological pre-Roman Celtic king, the play has been widely adapted for the stage and motion pictures, with the title role coveted by many of the world's most accomplished actors.
King Leir is an anonymous Elizabethan play about the life of the ancient Brythonic king Leir of Britain.
 It was published in 1605 but was entered into the Stationers' Register on 15 May 1594.
 The play has attracted critical attention principally for its relationship with "King Lear", Shakespeare's version of the same story.
Sir Matthew Brend (6 February 1600 – 1659) inherited from his father, Nicholas Brend, the land on which the first and second Globe Theatres were built, and which Nicholas Brend had leased on 21 February 1599 for a 31-year term to Cuthbert Burbage, Richard Burbage, William Shakespeare, Augustine Phillips, Thomas Pope, John Heminges, and William Kempe.
 During much of the time he was the legal owner of the Globe, Matthew Brend was underage, and his properties were managed for him by Sir Matthew Browne, John Collet, Sir John Bodley, and Sir Sigismund Zinzan.
 In 1623 Brend conveyed the property on which the Globe was built to his wife, Frances, as part of her jointure.
 In 1632 he was sued in the Court of Requests by the remaining original lessee, Cuthbert Burbage, and others, for an extension of their original lease.