Is Meursault capable of love?

The simple answer is we do not know. But irrespective of whether or not Meursault does have a capacity for love, there is little doubt that he does not display much in the way of loving behavior toward anyone, at least not in the conventional sense. Meursault shows all the signs of being a sociopath, and those afflicted with this personality disorder tend not to be the most loving of individuals.
Later on in the story, Meursault finds himself on trial for his flouting of established social conventions as much as for the Arab's murder. The prosecutor presents Meursault's relationship with his girlfriend Marie as existing purely to satisfy his own carnal lusts. The prima facie evidence for this contention is quite overwhelming. After a night of passionate lovemaking, Meursault calmly tells Marie that it did not mean anything. The prosecutor also makes hay with Meursault's borderline sacrilegious indifference to his late mother.
However, if we delve a little deeper, a more complex picture begins to emerge. There are a number of examples in the story where Meursault appears to show some semblance of true feeling towards Marie. Whether we can call it love is a moot point, but at the very least, it gives a more rounded picture of this most mercurial of characters. For instance, when the chaplain asks him if he ever sees the face of God in the prison walls, Meursault replies that the only face he looks for is Marie's. His actions are in vain, too.
Perhaps Meursault is lying to himself when he expresses the opinion that love is just a meaningless, abstract concept. The question of whether or not we accept that Meursault is capable of love boils down to the further question of whether we agree with him that love is indeed just an abstract concept or whether we feel that it has a much deeper meaning that Meursault himself chooses to overlook in his relationship with Marie.