The "Buddha", that is to say, teh Buddha Guatama was Nepalese.Buddhism started 2500 years ago in India
From there, the concepts moved into and developed in India. Later, the mahayana school moved into China and abroad.
But the older forms of Buddhism (therevada) are found in Nepal and Tibet.
Chan is a sect of buddhism that sprang up at Shaolin temple and so, that form of Buddhism, from a pure border perspective, is Chinese in origin.
But then, many people know nothing of the CHinese practice of Ch'an and more readily understand the idea of the Japanese Zen.
It is probably best to not associate buddhism with a nation though in the end. Its a practice and way of life that anyone of any religion can ake part in.
All they need to recognize is the 4 noble truths.
All they need to practice is the 8 fold path.
the 4 and the 8 fit with pretty much any other morality lessons in my opinion ergo making buddhist philosophy accessable to any and all persona who practiecs some other form of religiosity.