What is the central action of the play and how did Brutus deceive Caesar?

The central action of the play is the assassination of Julius Caesar at the Senate House on the Ides of March. Despite being a close friend of Caesar, Brutus plays a major part in this brutal murder. Like many of his fellow aristocrats he thinks that Caesar plans to make himself king of Rome, thus destroying the Republic. So he gets involved in the assassination plot, and even plunges a dagger into his old friend, who famously proclaims in Act III Scene i:

Et tu, Brute? (You too, Brutus?)

What this means is that Caesar can't believe that the man he always thought was his bosom buddy was capable of such murderous treachery. We can see from Caesar's shocked reaction that he's completely taken in by Brutus. This would indicate that Brutus had been able to keep up his facade of friendship with Caesar while all the while being involved in a plot to kill him.
Brutus is a Stoic, a follower of an ancient school of philosophy that teaches one to endure pain and suffering without showing one's emotions. Brutus's stoicism thus allows him to avoid betraying any outward signs of what he's really thinking. That's why Caesar's so taken aback that his good friend would do such a terrible thing to him. Brutus's stoical poker-face has deceived him utterly.

The central action of the play takes place in Act 3, Scene 1, where Julius Caesar is assassinated on the Senate floor by the conspiring senators. After ignoring the nightmares of his wife, Calpurnia, and dismissing the soothsayer's warnings to "beware the Ides of March," Julius Caesar decides to travel to the Senate, where the other senators murder him.
The senator Cassius knew that Brutus was close to Caesar and was respected by the Roman citizens, which is why he persuades Brutus to join the conspirators. Brutus had always been a loyal supporter of Julius Caesar and was considered his close friend. However, Cassius was able to convince Brutus that Caesar wished to rule Rome as a monarch. Being an honorable man, Brutus makes the difficult decision to join the conspirators. Julius Caesar is completely caught off guard on the Senate floor and does not expect Brutus to betray him, which is why some of his last words are "Et tu, Bruté?" (Shakespeare, 3.1.85): "And you, Brutus?" Julius Caesar trusted that Brutus was a loyal friend, similar to Mark Antony, and was astonished to discover that Brutus betrayed him.