In general relativity, how do we think of Newton's third law for gravity? In GR everything become geometric, gravity becomes curvature in spacetime.
How do we think of Newton's third law in the context of GR?
What corresponds to action and what to reaction?
 A: In general relativity, rather than a two objects exerting a gravitational force on each other, the two objects are both part of the stress-energy tensor.  This tensor determines the shape of spacetime (via the spacetime metric), and the spacetime metric determines what the geodesics are (roughly speaking, the metric determines how an object will move when no forces are acting on it), thus affecting the motion of objects.  
So, if you consider an apple and the Earth, the presence of both the apple and the Earth affect the spacetime metric, and this results in the apple and the Earth following paths that naively appear to be accelerated paths, but in fact are inertial paths through spacetime.
In that sense, they do both affect each other in a manner that is consistent with Newton's 3rd law, but because gravity is not a force in the context of GR, it doesn't make sense to analyze the situation using Newton's 3rd law.
A: The (strong) equivalence principle states that physics is the same as that of special relativity, in a local inetial frame. This means that conservation of 4-momemtum (ie. Newton 3rd law )  holds locally (point particles). In general notice that GR does not tell you anything new about non gravitational physics that you did not know already in SR.You obtain the laws in GR by applying to the SR laws the "comma goes to semicolon " rule. There are some rare exceptions where curvature coupling appears.
See MTW ch. 20 and 22 for details.
A: In GR everything become geometric, gravity becomes curvature in spacetime.
Actually, this isn't true. Spacetime curvature relates to the tidal force as opposed to the force of gravity. You will not find Einstein referring to a gravitational field as curved spacetime.     
How do we think of Newton's third law in the context of GR? What corresponds to action and what to reaction?
I don't think there's any consensus on this, but here's what I think: you'll be aware that any concentration of energy causes gravity, even a photon? And that for a photon, we say E=hf where h is Planck's constant of action? The gravitational field is the reaction to the action. Check out the Dirac Large Numbers Hypothesis.  
Edit 3 May 2015: 
I should perhaps add that in GR we quote the expression $G_{\mu \nu} + \Lambda g_{\mu \nu}= {8\pi G\over c^4} T_{\mu \nu}$. 
$T_{\mu \nu}$ is the stress-energy-momentum tensor which "describes the density and flux of energy and momentum in spacetime". $G_{\mu \nu}$ is the Einstein tensor which is related to the metric tensor wherein "empty space in its physical relation is neither homogeneous nor isotropic, compelling us to describe its state by ten functions (the gravitation potentials $g_{\mu \nu}$)". See Einstein talking about it here. In brief, when you place some concentration of energy in erstwhile empty space, it alters the surrounding space such that we then have a gravitational field.      
