How can I adjust the base year of this price index? I am given the following data for GDP deflator:

1997: 100.0

1998: 100.8

1999: 102.5

2000: 109.9

2001: 112.5

2002: 115.9

2003: 119.7

2004: 122.1

2005: 126.5

...and so on.

Currently, 1997 is the base year. However, I would like to rescale this index so that 2002 is the base year. Could I do this simply by solving 115.9-x=100 (x=15.9) and then subtracting 15.9 from each annual value? That is, would the following index be equivalent:

1997: 84.1

1998: 84.9

1999: 86.6

2000: 94.0

2001: 96.6

2002: 100.0

2003: 103.8

...and so on.
No, you want to re-scale proportionally, so you want to solve the equation $115.9x=100$, so that $x=100/115.9$ and then multiply each value by $x$. The value for 1997, for example, should be 86.3 (after rounding).