The "smooth silver case" in which Haines carries his cigarettes befits a man who “comes from Oxford,” and the "green stone" that sparkles amid the grey metal, like Ireland in the sea, symbolically suits the Englishman's status as "the seas’ ruler." Haines graciously offers Stephen a cigarette from the case, his noblesse obliging him to share his wealth with the impoverished Irishman next to him, even as he apologizes for the injustices of history.
Joyce's choice of this image as a symbol for British imperial domination of Ireland was probably inspired by a notorious gift that King Henry II of England received in 1155 from Pope Adrian IV, a.k.a. Nicholas Breakspear, the only English cleric ever elevated to the papacy. In the work called Metalogicus, the English cleric and scholar John of Salisbury writes that he delivered to Henry the infamous bull that begins Laudabiliter, giving him temporal rule over Ireland, along with a gold ring containing an emerald stone to signify the overlordship. The history of this exchange (as well as the authenticity of Laudabiliter) is murky and contested, but Oxen of the Sun shows that Joyce knew of the bull, and also of the story of the ring: "It is that same bull that was sent to our island by farmer Nicholas, the bravest cattle breeder of them all, with an emerald ring in his nose."
In an essay titled Fenianism: The Last Fenian (1907) Joyce wrote sardonically, "But the Pope meant nothing discourteous by this. Anyhow the Irish are so accommodatingly affable that they would hardly even grumble if tomorrow, owing to some unforeseen complication in Europe, the Pope having already given it to an Englishman, were to hand their island over to some temporarily unemployed hidalgo from the court of Alphonso."
The green stone from Stephen's first chapter makes an interesting return in Bloom's first chapter, reappearing in the face of Bloom's cat: "He watched the dark eyeslits narrowing with greed till her eyes were green stones." Perhaps the most important word here is "greed": the cat's hunger seems to draw the English lust for conquest back into the narrative.