Assign multiple objects to .GlobalEnv from within a function

Update of 2018-10-10:

The most succinct way to carry out this specific task is to use list2env() like so:

## Create an example list of five data.frames
df <- data.frame(x = rnorm(25),
                 g = rep(factor(LETTERS[1:5]), 5))
LIST <- split(df, df$g)

## Assign them to the global environment
list2env(LIST, envir = .GlobalEnv)

## Check that it worked
ls()
## [1] "A"    "B"    "C"    "D"    "df"   "E"    "LIST"

---

Original answer, demonstrating use of assign()

You're right that assign() is the right tool for the job. Its envir argument gives you precise control over where assignment takes place -- control that is not available with either <- or <<-.

So, for example, to assign the value of X to an object named NAME in the the global environment, you would do:

assign("NAME", X, envir = .GlobalEnv)

In your case:

df <- data.frame(x = rnorm(25),
                 g = rep(factor(LETTERS[1:5]), 5))
LIST <- split(df, df$g)
NAMES <- c("V", "W", "X", "Y", "Z")

lapply(seq_along(LIST), 
       function(x) {
           assign(NAMES[x], LIST[[x]], envir=.GlobalEnv)
        }
)

ls()
[1] "df"    "LIST"  "NAMES" "V"     "W"     "X"     "Y"     "Z"