Compiling a C program on Linux and running it under Windows

I have a compiled C program file -- say, simple.o -- the object file created on compilation from Red Hat Linux. Now I want this object file to be executed under Windows.

What's the way out for this? Is there any software that interoperates between these two?
Using your Web browser, download from www.cygwin.com and install the GCC compiler. Now you can compile your C program just like under Linux and run it on Windows inside the Cygwin toolkit.