After rotating a CALayer using CABasicAnimation the layer jumps back to it’s unrotated position

Have you set the removedOnCompletion property of the rotation animation to NO, e.g.,

rota.removedOnCompletion = NO;

That should leave the presentation layer where it was when the animation finished. The default is YES, which will snap back to the model value, i.e., the behavior you describe.

The fillMode should also be set, i.e.,

rota.fillMode = kCAFillModeForwards;