Sony A77 II has a Sony/Minolta Alpha lens mount and currently there are 143 native lenses available for this mount.
A77 II also has a sensor based image stabilization system which means that all of these lenses will be stabilized when used on A77 II.
Since Sony A77 II has a APS-C sensor, it has a focal length multiplier of 1.5x so you have to multiply lenses original focal length with this multiplier to find the Full Frame equivalent focal length of the lens when mounted on A77 II.
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Sony A77 II Lenses with Image Stabilization
Sony A77 II Lenses with Weather Sealings