A google search found this demo of a mirror in the BGE Video:Mirror Made in Blender Game Engine but I can't find out how to setup the material. Unlike in the BI renderer the option Mirror isn't available when in BGE.
What tricks do I need to know?
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You can easily fake it for Multitexture and GLSL - shading modes:
To make it work, you should use a sphere map and use camera view. I did this sphere map by setting the camera to orthographic (Orthographic Scale of 2.0, because the sphere is 2 blender units in diameter) and rendering a reflective sphere.
The result looks like this: