Cillian Murphy did not receive an Oscar nomination for portraying Robert Capa in Sunshine.
Cillian Murphy plays the mission's physicist there to operate the giant bomb which will revive the sun. Sunshine takes a similar approach to Alien, although does not do it nearly as well, in that it attempts to portray the crew of this spacecraft of science fiction in a down to earth way. This means that Cillian Murphy's Robert is only just about the lead since he does have to most personal focus in the film, but the early scenes in particular gives a fair amount of time to the the characters besides Capa. There is an interesting dynamic found with Murphy as Robert since he almost seems to have someone else vying for the lead role with Chris Evans's Mace, who is kinda the Charlton Heston there almost there to be someone who we know exactly where he stands since he makes it abundantly clear himself. The former and future superhero though is not the lead, even if he might be in most films, here instead we get Murphy as the lead who perhaps is best known for playing the Scarecrow in Batman Begins.
This is not Murphy going against his assumed type as the villain thanks to his angular and often gaunt looking appearance, although Capa is not a villain here. Murphy though does seem out of place in a heroic crew, and this works as just a visual way to show his distance from the rest of the crew since he is not an astronaut by profession. He simply does not fit in and Murphy amplifies this all the more with his distance he creates in his interactions with the other crew. Murphy does not play this as though Robert is trying to purposefully be cold or unfriendly with them, rather he exudes a natural discomfort fitting for a man who has simply lived a different life than his current comrades. This helps establish Robert's position on the ship where he's not the captain, and in no way is looked upon as a superior by the other, but he is given final say on the most important matters due to his expertise. Murphy creates this interesting dynamic in quite an effective though understated way as he makes Robert a separate sort from the rest.
The early scenes due somewhat reduce Murphy role because of this though since he does not interact all that much, that is until it decided that they should take a drastic action to potentially ensure the success of the mission. The decision is given to Robert and he rather bluntly makes the decision, along with a few other decisions of similar gravity throughout the film. It's again an interesting take, certainly unusual for a lead character, as Murphy does bring the same sort of bluntness with his performance as he does not portray Robert really dwelling on them for more than a moment. It's a precision that Murphy suggests, but it does not feel as brutal as it feels though. Murphy does not play it as though Robert is some uncaring or evil man by any means. What Murphy does instead is play into the intelligence of his character, as he makes the decision Murphy always alludes to Robert's complete understanding of the mission that propels him to make his decision in such a fashion. It's unique because Murphy manages to avoid seeming cruel by successfully showing why Robert acts this way.
I suppose Murphy also eases this all the more through the scenes where we get Robert's personal view. Murphy is especially good in suggesting the internalized unease in Robert as they come closer to the mission. When things start to go awry Murphy gradually reveals these more outwardly, although he does well to show that Robert only reveals this when he's either alone, or the situation is intense enough that he can't hide it. Murphy's performance works in amplifying the various actions scenes through his honest portrayal of Robert's fear throughout these scenes. These work particularly well for Murphy as he shows that eve though Robert is a man who makes calculated decisions, he's still a normal man when it comes to the life or death situations in the story. Murphy is very moving by slowly losing that reserve and conveying what every loss does to Robert's emotionally. He keeps building this up until the final minutes of the film where Boyle's choice of excessive editing undercuts Murphy's performance. Even as it is obvious that Murphy is trying to do something emotional with the rather explosive finale, he simply can't because every one of his image gets spliced away every split second. The impact of his performance is severely diminished. Even with that underwhelming ending, which has nothing to do with Murphy's own work, this is still a fine performance.