On the same night that Troilus and Cressida finally consummate their love, Diomedes arrives from the Greek camp to tell Aeneas and the others of their offer to return Antenor in exchange for Cressida. Although Aeneas is loath to part Troilus from his new love, it is agreed that the exchange must be made. Troilus and Cressida, after a long night together at Pandarus' house, finally take leave from one another. While they are out, Aeneas, Diomedes and the others bear the bad news to Pandarus, who shares it with a despairing Cressida.
Troilus, ever true to Troy, determines that Cressida must be given to the Greeks. He meets with Cressida one last time, both to say farewell and to entreat her to be true to him, promising that they will be together in time. Cressida finds his repeated entreaties to "be true" noxious; Troilus explains, saying that she will meet many Greeks skilled in the tricks of courtiers. They swear allegiance and part. As tokens of their oath, Troilus gives Cressida and sleeve and she gives him a glove. Diomedes, who promises in Troilus' sight that he will satisfy his lust for Cressida when she is with him in the Greek camp, rudely interrupts their parting.
In the fields outside of Troy, the Greeks prepare for the great challenge between Ajax and Hector. While they wait, Cressida arrives. Agamemnon, seeing how beautiful Cressida is, declares his kingly right to kiss her. He takes his kiss and the rest of the Greeks follow suit. Cressida trades quips with the Greeks while they kiss her; when Ulysses asks her for a kiss she declines him saucily, for which he bitterly spites her.
Aeneas and Agamemnon then arrange the battle between Hector and Ajax, which begins. The fight ends without a clear victor; Hector declares an end to it on account of the fact that Ajax is half-Trojan and his cousin. Ajax accepts Hector's reason, and they end their battle as friends and retire to a feast in the Greek camp. Hector trades compliments with all of the eminent Greeks until he comes to Achilles. They exchange threats and determine to meet one another in the field of battle the next day. Meanwhile, Troilus asks Ulysses where Calchas' tent is located, leading Ulysses to determine that Troilus is Cressida's lover. Ulysses promises to take Troilus to the tent under cover of darkness that night.
Finally, after three acts, a Trojan and a Greek meet on the field of battle. This meeting, however, is absurdly short - only a few passes, almost for ceremony's sake. Then, as in the earlier acts, war gives way to talk. Lots of talk. Hector, Nestor, Agamemnon, and even Ajax partake in sessions of extreme mutual admiration. One can see them making heroes of each other, praising themselves by praising their foes. The process of "heroicizing" is a constant source of fascination for Shakespeare.
Act Four not only brings Trojan and Greek together, it also brings the two strands of the plot - Troilus and Cressida / Ulysses and Achilles - together. The "kissing scene," when Cressida enters the Greek camp and allows the Greeks, whether under duress or not, to kiss her, is infamous. It is one of those moments in Shakespeare that could be played any number of ways. The ambiguity inherent in the situation is heightened by the fact that Cressida is largely silent throughout the scene. This is one of those key scenes - others can be found in The Taming of the Shrew and Titus Andronicus, as well as elsewhere - where the leading woman becomes silent at a moment of high drama, just as she is the center of attention. One might say that Cressida, upon entering the Greek camp, is truly objectified. Her agency is clearly compromised, but how to play that compromise is a matter of much debate.
Claire M. Tylee, in "The Text of Cressida and Every Ticklish Reader: Troilus and Cressida, The Greek Camp Scene," records a number of ways in which the kissing scene has been played. She notes that some critics, such as Joyce Carol Oates, have seen the scene as evidence that the Cressida of legend - the False Cressid - is Shakespeare's Cressida as well, and that these critics tend to vilify Cressida beginning with the kissing scene. Others play the scene more subtly, indicating that Cressida, as a female prisoner of war, has essentially no rights whatsoever; she depends upon the Greeks to protect her, and if she has to use her sexuality to secure protection, she will do so. The Greek camp, in this reading, is no place for the moony-eyed vows of Troilus; it is a place where the threat of rape and death is imminent. The complexities of Cressida's character only increase in the final act of the play.