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You have to overwrite the keyDown function in Stage.

See this example code

mStage = new Stage() {
        @Override
        public boolean keyDown(int keyCode) {
            if (keyCode == Keys.BACK) {
                Gdx.app.exit();
            }
            return super.keyDown(keyCode);
        }
    };
    Gdx.input.setInputProcessor(mStage);
    Gdx.input.setCatchBackKey(true);