I must disagree TEd.

There is nothing like an Aryan nation. There never has been in history even. The Third Reich interpretation was one put out by a bunch of impostors and poseurs. AS such, there cannot be affectations. The Swastika as used by the Nazis was an affectation, yes, but then, they were clearly impostors who were neither Aryans nor did they have a cultural legacy of the Swasitka.

Both the words Aryan and Swastikam are from Sanskrit.

Arya (pronounced, not as Aaryaaa, but as R-YUH), is a respectful way of addressing a gentleman.

Swastikam (SWUH-STHEE-KUHM), drives from Su (SUE) which means a general feeling of well-being, prosperity and goodness and Asthi (US-THEE), which means 'let it be'. Kam is a suffix indicating an object or a noun. Swasthikam therefore means, 'let general prosperity, and well-being prevail'. It is therefore, a symbolic representation of such a blessing. In Hinduism and some of its offshoot religions like Jainism and Buddhism, the Swasthikam is a very auspicious symbol and is used everywhere in India to signify just that. To this day, before the commencement of anything, from exams to enterprise, the swasthikam is drawn on the ground or some other surface, with an erasable red coloured powder and a small prayer is made to invoke blessings and good luck.

Till the Nazi misinterpretation, this symbol evoked images and feelings of nothing but auspiciousness and prosperity in all the cultures that used it. Never in the history of this symbol, has it ever been used as a sign of superemacy or racial authority.
Though the origin of this word is Sanskrit and Indian thereof, the same symbol is seen in other cultures, like Faldage mentioned, the Navajo Indians, Chinese, the Greeks, the Mayans, etc. The Chinese call it Wan, and I have seen in the walls of a Chinese temple in Kuching.

DDespite the Sanskrit derivation of the word Swastika, the origin of the symbol itself is contentious. Is it Aryan or Pre-Aryan (Indus Valley Harappan)? The time period given for the Swasthikam is 3000-1500 B.C., which period involves the overlap of both groups in its latter half.

The Nazi version had the Swastika at a salnt or an angle, whereas the traditional Swasthikam is always flat; can be right or left handed though.