I think it is important that everyone remember that:
Cardiac output = HR * stroke volume
The ejection fraction is not in the equation.
Stroke volume increases if there is an increase in end-systolic volume
or a decrease in end-diastolic volume. The ejection fraction is simply
a function of these.
A normal heart has an ejection fraction above 60%. Ejection fractions
lower than 60% mean the person is starting to have heart failure.
Ejection fractions less than 50% are associated with increased
mortality and ejection fractions less then 40% represent moderate to
severe heart failure.
If you start at 60% ejection fraction, it is impossible to double it
to 120%. This is why Carl Foster said the most liberal estimate would
be from 60% to 80%. Note that this is a 33% increase and not a 60%-80%
increase as Catherine Bacon says below.
And of course, there is the increased a-v extraction noted by previous
answers.
So, to keep it simple, the increase in VO2max comes partly from an
increase in cardiac output (which comes because of a mix of an
increase in stroke volume and HR), and an and partly from an increase
in a-v extraction.
Of course, we don't usually exercise at VO2max so the changes with
exercise may be very different when exercising at VO2 max vs
submaximal exercise. I went looking for a table at VO2max but couldn't
get one online. Here is a table from a paper in JAP in 2009 in middle-
aged men cycling at 60-65% of VO2max. Note that most of the increase
in stroke volume does come from ejection fraction in this table, and
cardiac output increases are therefore due to HR and "ejection-
fraction related increases in stroke volume". At very high heart rates
experienced at VO2max, there is less time for the heart to fill, end-
systolic volume therefore decreases, and this leads to decreases in
stroke volume (not sure if ejection fraction declines but I think so).