Shield TV, as switches to a 4k shader processing?

The pixel resolution is only 1920x1080 not 3840x2160. how can you, for example, reach the OpenGL variable “gl_FragCoord” outputs 4k values. Our apps only work with 4k who can possibly help?

Simpler GLSL fragment shader test proves NVIDIA Shield TV can not handle with 3840 pixels (4k) but only with 1920 pixels OpenGL.

main {
if (gl_FragCoord.x> 960.0) = gl_FragColor vec4 (1.0,0.0,0.0,1.0); // To pixel 0 - 960 red display
       else gl_FragColor = vec4 (0.0,1.0,0.0,1.0); // Green from pixel 961- maximum display
}

When connected 4k display this changes from red to green exactly in half, so maximum is 1920 pixels !!
It would at 3840 pixels, matrimonial change after 1 quarter from red to green.
Now, where is the problem, the hardware GPU OpenGL really only process FullHD, like all most 4k cheap TV boxes ???