Olympus E-M10 II has a Micro Four Thirds lens mount and currently there are 107 native lenses available for this mount.
E-M10 II also has a sensor based image stabilization system which means that all of these lenses will be stabilized when used on E-M10 II.
Since Olympus E-M10 II has a Four Thirds sensor, it has a focal length multiplier of 2x 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 E-M10 II.
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Olympus E-M10 II Lenses with Image Stabilization
Olympus E-M10 II Lenses with Weather Sealings