Yoga and Ayurveda are still relevant in many parts of the world and are not just specific to Hindu Nationalists. While the term "Islamic invasion" is not exactly correct, there is a dedicated Wiki page for Muslim conquests in the Indian subcontinent:

https://en.wikipedia.org/wiki/Muslim_conquests_in_the_Indian...

Since we are talking semantics seriously, even the British didn't "invade" India, they colonized it.