Swastik
The origins of the Swastik symbol are in India.
The name means 'good fortune' and, as Herman says, it's a symbol of auspiciousness.
If you've been to Thailand or Cambodia, you'll recall the national greeting 'Sawat-dee' which is the same word. (SE Asia received Buddhism from India).
Later on, the Tibetans, who were strongly influenced by Indian symbolism, absorbed it, and it became part of the pre-Buddhist Tibetan practice known as Bon.
Bon is an extremely powerful 'magic' which was subsequently combined with Tibetan Buddhism to create their unique style of religion and practice (only used for good). While Bon, conversely, was used for personal power.
The original Swastik is right-handed, ie clockwise.
The essential difference between that and the Bon symbol is that it's reversed, ie left-handed or anti-clockwise. Same as the Nazi application of it.
Hitler studied ancient Tibetan Bon traditions to use its power for personal gain. Mao did similar.
The connection with Native Americans is that some tribes had their origins in Tibet, as a result of migration across the Bering Straits.
That symbol came a long way before it appeared on that tyre in the CCM catalogue...